Method of High Spatial Resolution Determining a Position of a Singularized Molecule Which is Excitable for Emission of Luminescence Light

ABSTRACT

For spatial high resolution determining a position of a singularized molecule, which is excitable with excitation light for emission of luminescence light, in a sample, the excitation light is provided with an intensity distribution comprising an intensity increasing region with a known strictly monotonic course of an intensity of the luminescence light over a distance of the singularized molecule to a model point of the intensity distribution. The model point is arranged at different preliminary positions such that the intensity increasing region extends over a preliminary local area of the sample including the singularized molecule. From intensity values including intensities of the luminescence light separately registered for the preliminary positions of the model point, a further local area is determined which includes the singularized molecule and which is smaller than the preliminary local area. These steps are repeated using the last further local area as the next preliminary local area.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation to International ApplicationPCT/EP2017/075756 with an international filing date of Oct. 10, 2017entitled “Method for the high spatial resolution localization of anindividualized molecule which can be excited with excitation light inorder to emit luminescent light in a sample” and claiming priority toco-pending German Patent Application Nos. DE 10 2016 119 263.5, DE 102016 119 262.7, and DE 10 2016 119 264.3 all three entitled “Verfahrenzum räumlich hochauflösenden Bestimmen des Orts eines vereinzelten, mitAnregungslicht zur Emission von Lumineszenzlicht anregbaren Moleküls ineiner Probe” and filed on Oct. 10, 2016.

FIELD OF THE INVENTION

The present invention relates to a method of high spatial resolutiondetermining, in one or more spatial dimensions, a position of asingularized molecule which is excitable with excitation light foremission of luminescence light in a sample.

A singularized molecule which is excitable with excitation light foremission of fluorescence light is to be understood as a molecule here,that has a minimum distance to other similar molecules which areexcitable with the same excitation light for emission of fluorescencelight in a same wavelength range. This minimum distance is safely keptif the distances of the singularized molecules to such similar moleculesare at least as high as the diffraction barrier at the wavelength of theluminescence light. In this case, the luminescence light from thedifferent molecules which are excitable with the excitation light foremission of luminescence light can be registered separately. Theinvention, however, also includes embodiments in which this minimumdistance is smaller than the diffraction barrier at the wavelength ofthe luminescence light.

The luminescence light, for emission of which the singularized moleculeis excitable with the excitation light, may particularly be fluorescencelight. The emission of the luminescence light by the singularizedmolecule may, however, be based on any photo-physical process which isexcited by the excitation light. All processes of photoluminescence andalso, for example, an emission of luminescence light by quantum dotsexcited with the excitation light belong to these processes.

BACKGROUND OF THE INVENTION

The simplest method of determining a position of a singularized moleculewhich is excitable with excitation light for emission of fluorescencelight consists of actually exciting the molecule with the excitationlight for emission of luminescence light and of imaging the luminescencelight onto a camera or, more general, onto a spatially resolvingdetector. In principle, the diffraction barrier at the wavelength of theluminescence light applies to the spatial resolution achievable in thestep of imaging. If, however, a plurality of photons of the luminescencelight is detected with the spatially resolving detector, which areemitted by a single molecule at a fixed position in the sample, theposition of the molecule can be determined from the spatial distributionof these photons over the detector at a precision enhanced by a factorof 1/√{square root over (n)}, “n” being the number of the photonsregistered. Thus, a plurality of photons of the luminescence light whichare emitted by the singularized molecule and registered are aprecondition of clearly getting beyond, i. e. below the diffractionbarrier in this method which is designated as localization. Thus, thereis a danger that the singularized molecules are bleached during or evenprior to determining their positions in the sample at the desiredprecision. Particularly, a repeated determination of the position of thesame singularized molecule, as it is necessary for tracking a moleculemoving in a sample, is therefore often not possible.

If a singularized molecule emits luminescence light with a directionalspatial distribution, this has an influence on the determination of itsposition from the distribution of the photons of the luminescence lightover a spatially resolving detector, i.e. by means of localization,resulting in a position error. This position error depends on theorientation of the molecule in the respective sample. A directionaldistribution of the emitted luminescence light is, for example,displayed by molecules whose rotation diffusion times are longer than alifetime of their excited state out of which they emit the luminescencelight (see Engelhardt, J. et al. “Molecular Orientation AffectsLocalization Accuracy in Superresolution Far-Field FluorescenceMicroscopy”, NanoLett 2011 Jan. 12; 11 (1):209-13).

From WO 2006/127692 A2 it is known to mark a structure of interest in asample with activatable molecules which are in a non-fluorescentstarting state but which can be transferred with activation light into afluorescent state in which they are excitable with excitation light foremission of luminescence light. Thus, by means of the activation light,a sparse subset of the entirety of the molecules present can betransferred into the fluorescent state. In such a sparse subset, thenearest neighboring molecules in the fluorescent state are spaced apartby more than the diffraction barrier at the wavelength of the excitationlight, i.e. they are singularized. If the sample is then subjected tothe excitation light, fluorescence light is only emitted by thosemolecules in the fluorescent state. Thus, the fluorescence light fromthe individual singularized molecules in the fluorescent state can beregistered separately, and the positions of the individual molecules canbe determined by localization at a precision beyond the diffractionbarrier despite the higher absolute density of the molecules in thesamples. An image of the distribution of the molecules in the sample andthus of the structure of interest marked by them is achievedsuccessively in that the steps of activating a sparse subset of themolecules, of exciting the activated molecules for emission offluorescence light and of registering the fluorescence light with aspatially resolving detector until the respective activated moleculesare bleached are repeated and thus carried out for more and moremolecules marking the structure of interest.

WO 2006/127692 A2 also describes that the activation of a sparse subsetof the entirety of the molecules present, only, can be transferred toother imaging methods. Here, the singularized molecules can beselectively excited for emission of fluorescence light in certain planesor other spatial subunits of the sample by an intensity distribution ofthe excitation light having intensity maxima delimited by intensityminima.

The method known from WO 2006/127692 A2 is designated as PALM, i.e. asphoto-activated localization microscopy. A similar method designated asSTORM (stochastic optical reconstruction microscopy) principally has thesame advantages and disadvantages.

It is known from U.S. Pat. No. 8,174,692 B2 that even molecules of astandard dye which cannot be activated but have a fluorescent startingstate and which may also not be switched between two conformationstates, only one of which is fluorescent, may be used in determining thepositions of individual molecules by localization. For this purpose, thesample is subjected to such a high intensity of excitation light thatthe molecules are simultaneously transferred into a relatively longliving electronic dark state at a certain transfer probability so thatdistances of more than the diffraction barrier at the wavelength of thefluorescence light are adjusted between the molecules presently in thefluorescent state.

With the excitation light, the molecules which are presently in thefluorescent state are excited for emission of the fluorescence lightwhich is registered with a camera used as a spatially resolvingdetector. In this way, successively different molecules of the dye arelocalized as the molecules from which photons have already beenregistered get into the dark state out of which other molecules returnback into the fluorescent state at a certain transfer probability. Thisknown method may be executed continuously, i.e. one frames after theother may be read out of the camera in a continuous sequence, whereasthe sample is continuously subjected to the high intensity of theexcitation light which essentially keeps the dye in the dark state andsimultaneously excites the fluorescent molecule, which are singularizedin this way, for emission of fluorescence light.

The method known from U.S. Pat. No. 8,174,692 B2 is also designated asGSDIM (ground state depletion individual molecule return microscopy).

A principally different method of high spatial resolution determiningpositions of molecules which are excitable with excitation light foremission of luminescence light is applied in high spatial resolutionvariants of scanning fluorescence light microscopy. In scanningfluorescence light microscopy, the precision in determining thepositions of fluorescent molecules in a sample is based on that, at eachpoint in time, the sample is only locally excited for fluorescence suchthat the fluorescence light registered for the respective point in timecan be assigned to the local area of the excitation. If the molecules inthe sample are excited with focused excitation light, the diffractionbarrier at the wavelength of the excitation light sets the lower limitfor the spatial extensions of the local area of the excitation and thusfor the spatial resolution which can be achieved in imaging a structuremarked with the fluorescent molecules in the sample.

In STED (stimulated emission depletion) fluorescence light microscopy,molecules by which a structure of interest is marked in a sample areexcited by focused excitation light but directly de-excited again in thesurroundings of each measuring point by directed emission. This directedemission is stimulated by STED light and inhibits the emission offluorescence light by the molecules. Fluorescence light registeredafterwards may therefore only be emitted out of that area in which theexcited molecules have not been de-excited again by means of the STEDlight. This area in which the excited molecules have not been de-excitedagain may be kept very small in that it is defined by a zero point ofthe intensity distribution of the STED light and in that the maximumintensity of the STED light in intensity maxima delimiting the zeropoint is set so high that the excitation of the molecules is eliminatedcompletely, even very close to the zero point.

Instead of de-exciting a previous excitation of the molecules in partsof the sample, fluorescence inhibition light comprising an intensitydistribution having a zero point may also be used to switch fluorescentmolecules outside the zero point into a non-fluorescent dark state.This, for example, occurs in RESOLFT (reversible saturable opticalfluorescence transitions) microscopy or in GSD (ground state depletion)fluorescence light microscopy.

In the methods known as STED, RESOLFT or GSD fluorescence lightmicroscopy, every molecule, already before fluorescence light emitted byit is registered, in addition to the excitation light, is subjected tothe high intensities of the fluorescence inhibition light in theintensity maxima delimiting the zero point of the fluorescenceinhibition light. This causes a considerable danger of bleaching themolecules. The danger of bleaching also exists, if a singularizedmolecule which can be excited with excitation light for emission ofluminescence light is tracked with the zero point of the fluorescenceinhibition light according to these methods, as a rate of photons of theluminescence light emitted by the singularized molecule has to becontinuously maximized for this purpose.

From WO 2012/171999 A1 a method is known in which a sample is scannedwith an excitation beam of light which is superimposed with an intensitydistribution of STED light comprising a minimum at the focus of theexcitation beam of light so quickly that, in each of a plurality ofsubsequent scanning steps, fluorescence light is only registered in formof individual photons each of which having been emitted by an individualmolecule. The positions of the different individual molecules by whichthese photons have been emitted are assigned to the associated positionsof the minimum of the STED light in the sample.

In this method, only few photons, in an extreme case only a singlephoton is registered for each molecule to which a position in the sampleis assigned. These molecules, however, are nevertheless typicallysubjected to some cycles of excitation and stimulated emission so thatbleaching them is not excluded. Further, it is not possible topurposefully track a certain singularized molecule by means of thisknown method.

A method of tracking an individual fluorescent molecule is known from DE10 2011 055 367 A1, corresponding to U.S. Pat. No. 9,291,562 B2. Theindividual fluorescent molecule is excited with excitation light foremission of fluorescence light, and the fluorescence light isregistered. The excitation light is directed onto the sample with anintensity distribution comprising a local minimum, and the moleculemoving in the sample is tracked with the minimum. For this purpose, theintensity distribution of the excitation light is continuously shiftedwith regard to the sample so that a rate of photons of the fluorescencelight emitted by the molecule is minimized. This means holding themolecules in the minimum of the intensity distribution of the excitationlight, which may be a zero point of the intensity distribution of theexcitation light.

A method of determining the positions of singularized molecules in asample, wherein the singularized molecules are in a fluorescent state inwhich they are excitable with excitation light for emission offluorescence light, and wherein distances between the singularizedmolecules of the substance keep a minimum value is known from WO2015/097000 A1, corresponding to U.S. Pat. No. 9,719,928 B2. Thesingularized molecules are excited with the excitation light foremission of fluorescence light, wherein an intensity distribution of theexcitation light has a zero point. The fluorescence light from theexcited singularized molecules of the substance is registered fordifferent positions of the zero point of the intensity distribution ofthe excitation light in the sample. Here, distances between nearestneighboring positions of the zero point are not higher than half aminimum value of the distance of the singularized molecules.Particularly, the sample is scanned with the zero point, wherein aspacing in scanning the sample is not larger than half the minimumvalue. The positions of the singularized molecules in the sample arededuced from a course of the intensity of the fluorescence light fromthe respective singularized molecule over the positions of the zeropoint of the intensity distribution of the excitation light. For thispurpose, a function comprising a zero point can be fitted to the courseof the intensity of the luminescence light from the respectivesingularized molecule; and the position of the zero point of the fittedfunction can be taken as the position of the respective molecule. Thefunction can be a quadratic function. The fitted function may, however,individually be adapted to the intensity course of the luminescencelight from a singularized molecule of the respective substance whichresults from the intensity course of the excitation light in thesurroundings of its zero point.

In the method known from WO 2015/097000 A1, the respective singularizedmolecule, prior to getting into the neighborhood of the zero point ofthe intensity distribution of the excitation light in scanning thesample is subjected to the higher intensities of the neighboringintensity maxima of the excitation light. These intensities exceed asaturation intensity of the excitation light above which there is nofurther increase of the intensity of the luminescence light from therespective singularized molecules so that its course is constant at asaturation value and thus without information content. Correspondingly,very many photons are emitted by each singularized molecule of thesubstance before the photons are emitted from which the position of themolecule is determined. This causes a considerable danger of bleachingthe molecule even if only a limited number of photons is registered ateach position of the zero point of the excitation light before the zeropoint is shifted again.

A method of determining a distribution of a substance in a measurementarea by scanning the measurement area with a measurement front is knownfrom DE 10 2010 028 138 A1, corresponding to U.S. Pat. No. 9,024,279 B2.Over a depth of the measurement front which is smaller than thediffraction barrier at the wavelength of an optical signal, theintensity of the optical signal increases to such an extent that aproportion of the substance in a measurement state at first increasesfrom non-existing and then decreases again to non-existing. Themeasurement front is shifted over the measurement area in oppositedirection to the increase in intensity of the optical signal. Themeasurement signal which can be fluorescence light is registered andassigned to the respective position of the measurement front in themeasurement area.

There still is the need of a method of spatial high resolutiondetermining the position of a singularized molecule which is excitablewith excitation light for emission of luminescence light in a sample, inwhich the number of photons for the emission of which the singularizedmolecule has to be excited, in relation to the precision achievedtherewith is considerably reduced as compared to the known methods ofspatial high resolution determining the position of a singularizedmolecule.

SUMMARY OF THE INVENTION

The present invention relates to a method of spatial high resolutiondetermining, in n spatial dimensions, a position of a singularizedmolecule in a sample, the singularized molecule being excitable withexcitation light for emission of luminescence light, and n being 1, 2 or3. The method comprises providing the excitation light with an intensitydistribution which, in each of the n spatial dimensions, comprises atleast one intensity increasing region with a known strictly monotoniccourse of an intensity of the luminescence light from the singularizedmolecule over a distance of the singularized molecule to a model pointof the intensity distribution; determining a preliminary local area inthe sample which includes the singularized molecule; directing theexcitation light with the intensity distribution onto the sample;arranging the model point of the intensity distribution, in each of then spatial directions, at different positions in the sample; separatelyregistering the luminescence light emitted by the singularized moleculefor each of the different positions of the model point of the intensitydistribution in the sample; and deducing the position of thesingularized molecule in the sample from the intensities of theseparately registered luminescence light. Further, the following steps(i) and (ii) are repeated at least once using the last further localarea as the next preliminary local area: (i) in each of the n spatialdimensions, defining at least one preliminary position of the modelpoint of the intensity distribution such that the at least one intensityincreasing region associated with the respective one of the n spatialdimensions extends over the preliminary local area in the respective oneof the n spatial dimensions; and (ii) from intensity values of theluminescence light which include two intensity values for each of the nspatial dimensions, at least one of which being the intensity of theluminescence light registered for the at least one position of the modelpoint of the intensity distribution in the respective one of the nspatial dimensions, determining a further local area in the sample whichincludes the singularized molecule and which is smaller than thepreliminary local area.

The present invention also relates to repeated executions of the methodfor determining the positions of a plurality of molecules singularizedone after the other or for tracking the singularized molecule, and tousing a STED scanning fluorescence light microscope in carrying out orexecuting the method.

Other features and advantages of the present invention will becomeapparent to one with skill in the art upon examination of the followingdrawings and the detailed description. It is intended that all suchadditional features and advantages be included herein within the scopeof the present invention, as defined by the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be better understood with reference to the followingdrawings. The components in the drawings are not necessarily to scale,emphasis instead being placed upon clearly illustrating the principlesof the present invention. In the drawings, like reference numeralsdesignate corresponding parts throughout the several views.

FIG. 1 schematically shows an STED microscope which may be used forcarrying out the method for determining the position of a singularizedmolecule which is excitable with excitation light for emission ofluminescence light.

FIG. 2 shows a section through an intensity distribution of excitationlight comprising a zero point with adjacent intensity maxima, which, incarrying out the method with the STED microscope according to FIG. 1, isdirected onto a sample, and resulting intensities of luminescence lightwhich is emitted by the luminescent molecule located at respectivepositions in the sample.

FIG. 3 illustrates an execution of the first embodiment of the methodwith regard to a limited two-dimensional local area in the sample, inwhich the singularized molecule is presumably located.

FIG. 4 illustrates the relations between different intensities of theluminescence light registered in carrying out the first embodiment ofthe method for different positions of the zero point of the intensitydistribution of the excitation light in the sample.

FIG. 5 is a block diagram of a variant of the first embodiment of themethod.

FIG. 6 illustrates an execution of the second embodiment of the methodwith regard to a limited two-dimensional local area in the sample, inwhich the singularized molecule is presumably located.

FIG. 7, in a depiction corresponding to FIG. 4, illustrates therelations between different intensities of the luminescence lightregistered in carrying out the second embodiment of the method fordifferent positions of the zero point of the intensity distribution ofthe excitation light in the sample.

FIG. 8 is a block diagram of a variant of the second embodiment of themethod.

FIG. 9 illustrates a first execution of steps of the third embodiment ofthe method with regard to a first preliminary local area of thesingularized molecule in the sample.

FIG. 10 illustrates a second execution of the steps of the thirdembodiment of the method with regard to a further preliminary local areaof the singularized molecule in the sample, which has been reduced insize with regard to the first preliminary local area according to FIG.9.

FIG. 11 illustrates an alternative in executing the steps of the thirdembodiment of the method with a Gaussian intensity distribution of theexcitation light.

FIG. 12 illustrates two succeeding executions of the steps of the thirdembodiment of the method with a first relative arrangement of positionsof a model point of the intensity distribution of the excitation lightwith regard to the preliminary local areas.

FIG. 13 illustrates two succeeding executions of the steps of the thirdembodiment of the method with another relative arrangement of thepositions of the model point of the intensity distribution of theexcitation light with regard to the preliminary local areas.

FIG. 14 is a block diagram of a variant of the third embodiment of themethod for determining the position of a singularized molecule in asample.

FIG. 15 is a block diagram of a repeated execution of the thirdembodiment of the method for imaging a structure in a sample marked withsingularizable molecules; and

FIG. 16 is a block diagram of a repeated execution of the thirdembodiment of the method for tracking a movement of a singularizedmolecule in a sample.

DETAILED DESCRIPTION

In a first embodiment, a method of spatial high resolution determining aposition of a singularized molecule, which is excitable with excitationlight for emission of luminescence light, in one or more spatialdimensions in a sample comprises the following features: The excitationlight is directed onto the sample with an intensity distribution whichhas a zero point and regions of increasing intensity which adjoin ordelimit the zero point on both sides in each of the spatial dimensions.For each of different positions of the zero point in the sample, theluminescence light emitted by the molecule is registered, and theposition of the molecule in the sample is deduced from the intensitiesof the luminescence light registered for the different positions of thezero point. The zero point is arranged at not more than n×3 differentpositions in the sample to deduce the position of the molecule in nspatial dimensions from the intensities of the luminescence lightregistered for the different positions of the zero point.

In a second embodiment, a method of spatial high resolution determininga position of a singularized molecule, which is excitable withexcitation light for emission of luminescence light, in one or morespatial dimensions in a sample comprises the following features: theexcitation light is directed onto the sample with an intensitydistribution comprising a zero point and intensity increasing regionswhich adjoin the zero point on both sides in each of the spatialdirection. The zero point is shifted in the sample in each of thespatial dimensions, and luminescence light emitted by the molecule isregistered for each position of the zero point in the sample. A startinglocal area in the sample is determined in which the molecule isarranged. In each of the spatial dimensions, at least one startingposition of the zero point is determined such that it is on one side ofthe starting local area in the respective spatial dimension. Theluminescence light is quasi-simultaneously registered for all positionsof the zero point assigned to all spatial dimensions in that the zeropoint is repeated shifted between these positions. The positions of thezero point are successively shifted into the starting local areadepending on the photons of the luminescence light registered for eachof the positions.

In a third embodiment, a method of spatial high resolution determining aposition of a singularized molecule, which is excitable with excitationlight for emission of luminescence light, in one or more spatialdirections in a sample comprises the following features: the excitationlight is directed onto the sample with an intensity distribution whichhas an intensity increasing region with known strictly monotonic courseof the intensity of the excitation light over a distance to a modelpoint of the intensity distribution in each of the spatial dimensions.The model point of the intensity distribution is arranged at differentpositions in the sample in each of the spatial dimensions. For eachposition of the model point of the intensity distribution in the sample,the luminescence light emitted by the molecule is registered, and theposition of the molecule in the sample is deduced from the intensitiesof the luminescence light registered. Particularly, a starting orpreliminary local area in the sample is determined in which the moleculeis arranged. Then, (i) in each of the spatial dimensions, at least oneposition of the model point of the intensity distribution is definedsuch that the at least one intensity increasing region extends over thepreliminary local area in the respective spatial dimension. Further,(ii), from the intensity values of the luminescence light which includetwo intensity values per each of the spatial dimensions, one of whichindicating the intensity of the luminescence light registered for the atleast one position of the model point of the intensity distribution, afurther local area in the sample is determined in which the molecule isarranged and which is smaller than the starting local area. The steps(i) and (ii) are repeated at least once using the further local area asthe new preliminary local area.

In this specification and the appending claims, the formulation that themethod serves for spatial high resolution determining the position ofthe singularized molecule particularly means that a spatial resolutionclearly below the diffraction barrier at the wavelength of theexcitation light and also at the wavelength of the luminescence light isachieved which can be seen from the achievable precision of 10 nm andeven much better. In this context it is to be noted that the formulation“spatial resolution” is used as a synonym here for the precision atwhich the position of the respective singularized molecule in the sampleis determined.

The formulation that the method serves for determining the position of asingularized molecule means, as already stated at the beginning, thatthe position of the singularized molecule has a minimum distance tonearest neighboring similar molecules which can be excited with the sameexcitation light for emission of luminescence light in the samewavelength range so that the luminescence light from the nearestneighboring similar molecules can not be separated due to differentwavelengths. In all embodiments of the method, this minimum distance isof the order of the diffraction barrier at the wavelength of theluminescence light or smaller. In fact, this minimum distance, like inthe method known from WO 2015/097000 A1, may even be considerablysmaller than the diffraction barrier at the wavelength of theluminescence light as long as it is not smaller than an extension of anintensity increasing region of the intensity distribution of theexcitation light in the respective spatial dimension, over which theintensity of the excitation light is below a saturation intensity sothat the intensity of the luminescence light emitted by the respectivemolecule remains below a saturation value. If the distance of thesingularized molecule to nearest neighboring molecules excitable withthe excitation light for emission of luminescence light remains largerthan the diffraction barrier at the wavelength of the luminescencelight, the luminescence light emitted by the singularized molecule canbe registered separately from luminescence light emitted by the nearestneighboring molecules with a spatially resolving detector. If thedistance of the singularized molecules is at least not smaller than aregion of the intensity distribution of the excitation light which isinfluenced by the intensity increasing region with regard to theintensity of the luminescence light emitted by the molecules, thedifference of the intensity of the luminescence light registered to thesaturation value at the saturation intensity of the excitation light maydirectly be attributed or assigned to the singularized molecule as thismolecule is the only one which is in the region of the intensitydistribution of the excitation light influenced by the intensityincreasing region.

The formulation that the singularized molecule is excitable with theexcitation light for emission of luminescence light means that thesingularized molecule is photo-luminescent. Particularly, thesingularized molecule may be fluorescent, i.e. it may be excitable foremission of fluorescence light with the excitation light. At this pointit is to be pointed out that the terms “luminescent” and “fluorescent”here only indicate that the singularized molecule can be excited withthe excitation light for emission of luminescence light or fluorescencelight. The terms do not indicate that the singularized molecule isalready luminescing or fluorescing, i.e. that it has already beenexcited with the excitation light.

The formulation that the excitation light, in the first and secondembodiment of the method, is directed onto the sample with an intensitydistribution which has a zero point and intensity increasing regionswhich are delimiting or adjoining the zero point on both sides in eachof the spatial dimensions may mean that the zero point with theadjoining intensity increasing regions is formed by destructiveinterference which has a different effect at different distances to thezero point. Over each of the intensity increasing regions adjoining thezero point, the intensity of the excitation light strictlymonotonically, i.e. continuously, increases with increasing distance tothe zero point.

The zero point may be an ideal zero point generated by destructiveinterference in which the intensity of the excitation light actuallygoes down to zero. A small remaining or residual intensity of theexcitation light in the zero point, however, is harmless, particularlyas it is no goal of the first and second embodiment of the method toposition the zero point in the sample such that its position coincideswith the position of the molecule in the sample. For the same reason,the zero point delimited by the intensity increasing regions may inprinciple also be generated by Gaussian intensity distributions arrangedat a distance in the respective spatial dimension, and particularly bythe intensity minimum remaining between them.

Even with a two-dimensional zero point and intensity increasing regionsonly extending in a single spatial dimension, the position of themolecule in the sample can be determined at a high spatial resolution intwo or all three spatial dimensions. In a same way, with aone-dimensional or line-shaped zero point and intensity increasingregions only increasing in two spatial dimensions, the position of thesingularized molecule in the sample may not only be determined in thesetwo but also in all three spatial dimensions at a high spatialresolution. For this purpose, the intensity increasing region(s) is/areto be orientated in different spatial dimensions in executing the firstand the second embodiments of the method.

The present method may be regarded as starting from a method of spatialhigh resolution determining the position of a singularized molecule inone or more spatial dimensions in a sample, wherein the sample isexcitable with excitation light for emission of luminescence light,which is known from WO 2015/097000 A1.

In the first embodiment of the method, the excitation light, like in thestarting method, is directed onto the sample with an intensitydistribution comprising a zero point and intensity increasing regionswhich adjoin the zero point on both sides in each of the spatialdimensions. For each of the different positions of the zero point in thesample, the luminescence light emitted by the molecule is registered,and the position of the molecule in the sample is deduced from theintensities of the luminescence light registered for the differentpositions of the zero point.

Different from the known method, the zero point, in the first embodimentof the method, is arranged at not more than n×3 different positions inthe sample to deduce the position of the molecule in the n spatialdimensions from the intensity of the luminescence light registered forthese different positions. In fact, it has been found that, with asuitable selection of the positions of the zero point in the sample, theposition of the molecule in the sample in the n spatial dimensions canbe deduced from the intensities of the luminescence light for not morethan n×3 different positions at a precision which is not lower than withspatially, i. e. completely, scanning the local area in the sampleincluding the position of the molecule. Further, with a suitableselection of the positions as it will be described in the following,this precision may already be achieved if the zero point is arranged atnot more than (n×2)+1 or even only n+2 different positions in thesample. Here, it is often not even necessary to increase the number ofphotons of the luminescence light registered for each of the positionsof the zero point in the sample as compared to the number of photonswhich are suitably registered at each position of the zero point inspatially scanning the sample.

Thus, in the first embodiment of the method, the position of thesingularized molecule in the sample is very quickly determined in eachspatial dimension, i.e. on basis of a very small number of photonsemitted by the singularized molecule and registered. The precision atwhich the position of the singularized molecule is determined maywithout problem reach 10 nm and thus clearly gets below the diffractionbarrier at the wavelength of the luminescence light.

As already mentioned, the sample is not scanned spatially, i. e.completely, not even in a limited local area of the sample in which themolecule is assumed in the first embodiment of the method. Instead thezero point is only positioned at very few positions with regard to, i.e. in or close to this local area.

In deducing the position of the molecule in the sample from theintensities of the luminescence light registered for the differentpositions of the zero point, the dependency of the intensity of theluminescence light which is emitted by the singularized molecule on thedistance of the singularized molecule to the zero point of the intensitydistribution of the excitation light has to be considered. Thisdependency results from the course of the intensity of the excitationlight in the intensity increasing regions adjoining the zero point andalso from the photo-physical process on which the excitation of themolecule for the emission of the luminescence light is based. Thus, witha zero point formed by destructive interference and a photoluminescenceof the molecule based on a single photon process the dependency of theintensity of the luminescence light emitted by the molecule on itsdistance to the zero point will approximately be quadratic. With aphotoluminescence on basis of a two photon process, this dependency isstronger and will follow a function x⁴. De facto, in the firstembodiment of the method, the course of the intensity of the excitationlight in the intensity increasing regions adjoining the zero point hasonly to be known to such an extent as it has an effect on the intensityof the luminescence light from the molecule. I.e. the dependency of theintensity of the luminescence light from the molecule on the distance ofthe molecule to the zero point has to be known to consider it indeducing the position of the molecule in the sample from the intensityof the luminescence light registered. This dependency, however, caneasily be determined, for example empirically by once scanning thesurroundings of a singularized molecule with the zero point in smallsteps.

Particularly, the position of the molecule can be deduced from theintensities of the luminescence light registered for the differentpositions of the zero point in that a function is fitted to theseintensities, which describes the course of the intensity of theluminescence light from the molecule over the distance of the moleculeto the zero point in the different spatial dimensions and which also hasa zero point. The position of the zero point of the fitted function inthe sample may then be taken as the position of the molecule.

The fact that the position of the molecule is deduced from theintensities of the luminescence light which is registered for thedifferent positions of the zero point does not only include the optionof considering different rates of photons of the luminescence light butalso the option of considering intervals in time at which the photonsare registered. Here, it is to be understood that the average value ofthe intervals in time at which the photons are registered is equal tothe reciprocal value of the rate of the photons of the luminescencelight registered for a respective position of the zero point.

In addition to the intensities of the luminescence light registered forthe different positions of the zero point, a measure of the relativeluminosity of the singularized molecule can be considered in deducingthe position of the molecule. This measure may particularly be a maximumintensity of the luminescence light emitted by the molecule when excitedwith the excitation light or an intensity value directly correlatedtherewith. The maximum intensity or the intensity value correlatedtherewith may indeed be measured for the respective singularizedmolecule or estimated for all potential singularized molecules with afixed value.

In order to do with a particularly small number of different positionsat which the zero point is arranged in the sample, the differentpositions can be arranged such that they, in each spatial dimension inwhich the position of the molecule and the sample is determined, includeone position on both sides of a center of the local area in the samplein which the molecule is arranged. This, however, does not mean that twoextra positions of the zero point have to be provided for each spatialdimension. For example, three positions which are arranged in thecorners of a particularly equilateral triangle in one plane also includeat least two positions in any spatial dimension within the plane, whichare arranged on different sides of the center point of the triangle. Thesame applies to an equilateral tetrahedron with regard to all possiblespatial dimensions.

In the first embodiment of the method, it is further preferred if thedifferent positions at which the zero point is arranged in the sample,besides the two positions on both sides of the center of the local area,include a position in the center of this local area in each spatialdimension in which the position of the molecule in the sample isdetermined. This one position in the center of the local area may be thesame one for all spatial dimensions.

Particularly, in that case that the position of the molecule isdetermined in two spatial dimensions, the different positions at whichthe zero point is arranged in the sample may be a center position andthree peripheral positions, i.e. four positions in total, the peripheralpositions being arranged on an arc of a circle around the centralposition in a plane spanned by the two spatial dimensions and runningthrough the central position. In other words, the three peripheralpositions are arranged in the corners of an equilateral triangle, andthe central position is in the center of the triangle.

When the position of the molecule is determined in all three spatialdimensions, the different positions at which the zero point is arrangedin the sample may include a central position and four peripheralpositions, the peripheral positions being equidistantly arranged on aspherical shell around the central position. In other words, theperipheral positions are arranged in the corners of an equilateraltetrahedron, and the central position is in the center of thetetrahedron.

As already mentioned, the entire local area of the sample in which themolecule is assumed should, with regard to each position of the zeropoint, be in a region of the intensity distribution of the excitationlight in which the intensity in the intensity increasing regionsadjoining the zero point remains below the saturation intensity of theexcitation light above which a further increase of the intensity of theexcitation light does no longer result in a higher intensity of theluminescence light from the singularized molecule. In the firstembodiment of the method it is preferred that a maximum intensity, i.e.an absolute intensity level of the excitation light, is always adjustedsuch that a maximum distance of each position of the zero point to anypoint between the positions of the zero point in the sample is nothigher than an extension of each intensity increasing region in thedirection of the distance. It is even more preferred if the maximumdistance is not larger than an extension of each intensity increasingregion in the direction of the distance over which the intensity of theexcitation light increases up to 90% of a saturation intensity of theexcitation light.

In the first embodiment of the method, the intensity increasing regionsadjoining the zero point may be rotation-symmetric with regard to thezero point. At least, this rotation-symmetry may be given in a mainplane orthogonal to that direction in which the excitation light isdirected onto the sample. It is, however, also possible that theexcitation light differs with regard to its wavelength and/or itspolarization, and/or the intensity regions adjoining the zero point inthe different spatial dimensions differ with regard to the course of theintensity of the excitation light depending on the respective positionof the zero point. This may be be the case to pursue the goal todetermine the position of the molecule at each point between thepositions of the zero point in each of the spatial dimensions at a sameprecision. It is, however, to be understood that in this case themaximum possible precision in determining the position of thesingularized molecule is not completely exploited in certain spatialdimensions. Vice versa, each singularized molecule represented by a spothaving the extensions of the precision achieved appears as a smallcircle or sphere, only if this precision is the same in all spatialdimensions.

In the first embodiment of the method, the luminescence light may bequasi-simultaneously registered for the different positions of the zeropoint in the sample in that the zero point is repeatedly shifted betweenthe positions in the sample. For this purpose, the same intensitydistribution of the excitation light may be shifted by means of scanner.It is, however, also possible to separately form the intensitydistribution for each of the different positions of its zero point inthe sample, for example by means of a spatial light modulator arrangedin the beam path of the excitation light. Then, one may at least insofardo without a scanner. Further, it is possible to shift the zero point inthe sample in that the excitation light is one after the other providedby completely or partially different light sources. With all thesepossible variants of the first embodiment of the method, the zero pointcan be repeatedly shifted between its positions in the sample. It is tobe understood that the luminescence light from the molecule belonging tothe individual positions of the zero point is registered separately. Thequasi-simultaneous registration of the luminescence light for thedifferent positions of the zero point has the advantage that subjectingthe sample to the excitation light and registering the luminescencelight from the sample may be stopped or aborted as soon as the photonsof the luminescence light registered for the individual positions of thezero point already allow for deducing the position of the molecule at adesired precision from the intensities of the luminescence lightregistered for the different positions of the zero point.

A corresponding abort criterion may also be applied with a continuousregistration of the luminescence light for each position of the zeropoint in the sample. There are, however, cases in which the luminescencelight registered for all positions of the zero point already indicatesafter a lower total number of photons from the molecule that theposition of the molecule may be deduced at the desired precision.

If, in the first embodiment of the method, the luminescence light isregistered for the positions of the zero point of the intensitydistribution of the excitation light only until the intensities of theluminescence light registered for the positions are determined at suchan accuracy that the position of the molecule can be deduced at adesired precision, this desired precision can be in the range of 20 nmor smaller, i. e. better. It may also be smaller or better than 10 nm.Even a desired precision in the order of 1 nm and thus down to 0.5 nm ispossible. In principle, the first embodiment of the method has noinherent barrier to the precision achievable in determining the positionof the singularized molecules in the sample. Circumstances of therespective individual case like, for example, a decreasingsignal-to-noise-ratio may, however, limit the precision achievable inpractice.

A repeated execution of the first embodiment of the method withdecreasing distances of the positions of the zero point in the sample,wherein the positions of the zero point in the sample, in eachrepetition of the method, are arranged around the position of themolecule in the sample which has been deduced in the previous executionof the method from the registered intensity of the luminescence light,may serve for iteratively increasing the precision achievable with thefirst embodiment of the method. With the distances between the positionsof the zero point in the sample getting smaller, the maximum intensityof the excitation light may be increased. In this way, the gettingsmaller limited local area in which the molecule is presumably locatedmay then again be spread over the full bandwidth of the differentintensities of the excitation light in the intensity increasing regionsand thus over the full bandwidth of the different intensities of theluminescence light from the singularized molecule. In the secondembodiment of the method, the excitation light, like in the startingmethod known from WO 2015/097000 A1, is directed onto the sample with anintensity distribution which has a zero point and intensity increasingregions which adjoin or delimit the zero point in each of the spatialdimensions on both sides. This zero point is shifted in the sample ineach of the spatial dimensions, and for each position of the zero pointin the sample the luminescence light emitted by the molecule isregistered separately.

In the second embodiment of the method, in addition to the known method,at first an initial or preliminary local area in which the molecule islocated in the sample is determined. Then, in each spatial direction, atleast one preliminary position of the molecule is defined such that itis on one side of the preliminary local area in the respective spatialdimension. The luminescence light is quasi-simultaneously registered forall the positions of the zero point associated with all spatialdimensions in that the zero point is repeatedly shifted between thesepositions, and the positions of the zero point are successively shiftedinto the preliminary local area depending on the photons registered foreach of the positions.

In this way, the positions of the zero point assigned to all spatialdimensions are very quickly, i.e. on basis of a very low number ofphotons emitted by the singularized molecule and registered,approximated to the actual position of the molecule in the sample, andthus condensed to a local area of a strongly reduced size as compared tothe preliminary local area. The extensions of the strongly reduced localarea correspond to a precision at which the position of the singularizedmolecule is determined. These extensions may without problem get smallerthan 10 nm and thus clearly below the diffraction barrier at thewavelength of the luminescence light.

In the second embodiment of the method, the sample, even in thepreliminary local area of the molecule, is not scanned spatially, i. e.completely. Instead, the positions of the zero point of the intensitydistribution are shifted towards the actual position of the moleculebased on the photons of the luminescence light registered for theprevious positions of the zero point of the intensity distributionintelligently, i.e. exploiting all information available from theregistered photons of the luminescence light up to now with regard tothe actual position of the singularized molecule to a maximum extent,and thus, as a rule, in one direction only. In the second embodiment ofthe method, the positions of the zero point are thus not shiftedaccording to a trial and error method but always in a direction towardsthe actual position of the molecule in the sample even if the positionsof the zero point will not necessarily be shifted along the shortestways to the actual position of the molecule.

In successively shifting the zero point, a measure of the relativebrightness of the singularized molecule can be considered to, forexample, determine a distance over which the zero point may be shiftedat a time. This measure can particularly be a maximum intensity of theluminescence light from the molecule when excited with the excitationlight, or an intensity value directly correlated therewith. The maximumintensity or the intensity value correlated therewith may be actuallymeasured for the singularized molecule or estimated with a fixed valuefor all potentially singularized molecules.

In the second embodiment of the method, the luminescence light for therespective different positions of the zero point in the sample isquasi-simultaneously registered in that the zero point is repeatedlyshifted between these different positions in the sample. For thispurpose, the same intensity distribution of the excitation light may beshifted by means of a scanner. It is, however, also possible toseparately form or generate the intensity distribution for each of thedifferent positions of its zero point in the sample, for example bymeans of a spatial light modulator arranged in the beam path of theexcitation light. Then, one may at least insofar do without a scanner.Further, it is possible to shift the zero point in the sample in thatthe excitation light is successively provided by different lightsources, completely or in parts. With all these variants of the secondembodiment of the method, the zero point can be very quickly repeatedlyshifted between its different positions in the sample. It is to beunderstood that the luminescence light from the molecule belonging tothe individual positions of the molecule is registered separately. Dueto the quasi-simultaneous registration of the luminescence light for thedifferent positions of the zero point of the intensity distribution ofthe excitation light, the subjection of the sample to the excitationlight and the registration of the luminescence light from the sample canimmediately be stopped as soon as the photons of the luminescence lightregistered for the individual positions of the zero point of theintensity distribution of the excitation light already allow forshifting the positions further towards the actual position of themolecule in the sample.

In the second embodiment of the method, the positions of the zero pointmay particularly be successively shifted into the preliminary local areadepending on rates or intervals in time at which the photons of theluminescence light are registered for each of the positions. Here, it isto be understood that the average value of the intervals in time isequal to the reciprocal value of the rate at which the photons of theluminescence light are registered for the respective position of thezero point of the intensity distribution of the excitation light. Thestep of purposefully shifting the positions of the zero point into thepreliminary area may for example at first pursue the goal to match therates or the corresponding intervals in time at which the photons of theluminescence light are registered for the individual positions to eachother. For this purpose, the position of the zero point for which thephotons of the luminescence light are registered at the highest rate orat the shortest intervals in time may be shifted in a direction towardsthe positions of the zero point with the smallest rates or the longestintervals in time. Simultaneously or afterwards, all positions of thezero points may be shifted into the preliminary local area to minimizethe rates or to maximize the intervals in time at which the photons areregistered for all of them. If, for example, the rates or the intervalsin time at which the photons are registered for all positions of thezero point have already been matched to each other, these positions mayfurther be shifted into the local area towards their common center tominimize the rates or maximize the intervals in time of the photons.

A number of the positions of the zero points, which are defined withregard to the preliminary local area and which are then shiftedaccording to the second embodiment of the method, may be between n and 2n, n being the number of spatial dimensions in which the singularizedmolecule is localized. I.e. the number of the positions of the zeropoint may be very small. At least one position of the zero point isneeded for each of the spatial dimensions, in which the position of themolecule in the sample is to be determined, to be able to purposefullyshift the entirety of the positions of the zero point on basis of thephotons of the luminescence light registered for them. With twopositions of the zero point per each spatial dimension, the actualposition of the molecule in the sample can be successively approachedfrom both sides as it will be explained below in more detail.

In the second embodiment of the method, in at least one of the spatialdimensions, the position of the molecule in the sample may be assumed atthat position of the zero point associated with the respective spatialdimension at which the rate or the intervals in time of the photons ofthe luminescence light emitted by the singularized molecule is minimalor maximal, respectively. In this variant of the second embodiment ofthe method, the respective zero point has to be shifted to coincide withthe molecule in the sample as good as possible.

In at least one of the spatial dimensions, the position of the moleculemay alternative be deduced from the rate or the intervals in time atwhich the photons of the luminescence light are registered for at leastone of the positions of the zero point associated with the respectivespatial dimension.

Herein, the dependency of the rate or the interval in time of thephotons of the luminescence light on the spatial distance of thesingularized molecule to the zero point of the intensity distribution ofthe excitation light is to be considered. This dependency results fromthe course of the intensity of the excitation light in the intensityincreasing regions and also from the photo-physical process which is thebasis of the excitation of the molecules for the emission of thefluorescence light. Thus, with an intensity increasing region adjoininga zero point formed by destructive interference and a photoluminescenceon basis of a one photon process there will be an approximatelyquadratic dependency of the intensity of the luminescence light emittedby the molecule on the distance to the zero point. With aphotoluminescence on basis of a two photon process, this dependency isstronger and follows a function x⁴. In practice, the course of theintensity of the excitation light in the intensity increasing region hasonly to be known insofar as it has an effect on the intensity of theluminescence light from the molecule. I.e. the dependency of theintensity of the luminescence light on the distance of the molecule tothe zero point of the intensity distribution of the excitation light hasto be known to be able to use it for the determination of the actualposition of the molecule in the sample. This dependency can be easilydetermined, for example empirically by scanning the surroundings of themolecule with the zero point in small steps.

In deducing the actual position of the molecule in the sample from therate or the distances in time of the photons of the luminescence lightwhich are registered for at least one position of the zero pointassigned to the respective spatial dimension, a further rate or furtherintervals in time of photons of the luminescence light may beconsidered. This may be a further rate or these may be further intervalsin time of photons of the luminescence light which are registered for afurther position of the zero point assigned to the respective spatialdimension. In this case, the distance of the positions of the zero pointin the respective spatial dimension has also to be considered.Alternatively or additionally, the already mentioned measure of therelative brightness of the singularized molecule may be considered indeducing the position of the molecule in the sample from the rate or theintervals in time at which the photons of the luminescence light areregistered for the at least one position of the zero point.

In a variant of the second embodiment of the method, the preliminarypositions of the zero point include two positions per each spatialdimension, which, in the respective spatial dimension, are located onboth sides of the preliminary local area. By successively shifting thepositions of the zero point assigned to all spatial dimensions dependingon the rates or the intervals in time at which the photons of theluminescence light are registered for all positions of the zero point, alocal area of the molecule remaining between the positions of the zeropoint is successively reduced in size. In doing so, there is no need topredetermine two separate or extra preliminary positions of the zeropoint per each spatial dimension. Instead, one of the preliminarypositions of the zero point may also be assigned to more than onespatial dimension. Thus, for example, the preliminary positions of thezero point for determining the position of the molecule in two spatialdimensions may be arranged in the corners of a triangle in a plane whichis defined by these two spatial dimensions, i.e. the preliminarypositions of the zero point may amount to just three positions in total.Correspondingly, the preliminary positions of the zero point fordetermining the position of the molecule in three spatial dimensions maybe arranged in the corners of a tetrahedron. Generally, it is, however,also possible to have two separate or extra positions of the zero pointper spatial dimension in which the position of the molecule isdetermined in the sample. With regard to the aspect of determining theposition of the molecule in the sample based on an as low number ofphotons of the luminescence light as possible, the resulting highernumber of positions of the zero point in the sample for which theluminescence light is registered, might, however, not be ideal.

Particularly, if the preliminary positions of the zero point in each ofthe spatial dimensions include two positions which are located on bothsides of the preliminary local area in the respective spatial dimension,it is preferred that the intensity increasing regions adjoining the zeropoint in each of the spatial dimensions are symmetric with regard to thezero point. It is even more preferred if the intensity increasingregions in all spatial dimensions in which the position of the moleculein the sample is determined are rotationally symmetric with regard tothe zero point.

The local area of the molecule remaining between the positions of thezero point may successively be reduced in size until its extensions areno longer larger than a predetermined precision. This predeterminedprecision may be in a range of 20 nm or smaller, i.e. better. It mayalso be smaller or better than 10 nm. Even a predetermined precision inthe order of 1 nm and thus down to 0.5 nm is possible. In principle, thesecond embodiment of the method has no inherent barrier to the precisionachievable in determining the position of the singularized molecule inthe sample. The circumstances of an individual case, like for example adecreasing signal-to-noise-ratio, however, may limit the precisionachievable in practice.

Thus, getting below a predetermined signal-to-noise-ratio may be definedas an abort criterion for further shifting the positions of the zeropoint in the second embodiment of the method. This signal-to-noise-ratiomay be enhanced by reducing the size of a pinhole aperture arranged infront of a point detector with which the luminescence light emitted bythe singularized molecule is registered confocally with regard to therespective position of the zero point in the sample. This reduction ofthe size of the pinhole aperture comes along with a reduction of theyield of photons registered as compared to the photons of theluminescence light emitted by the molecule. Thus, this reduction may belimited to the final positions of the zero point in the closestneighborhood of the actual position of the molecule in the sample inwhich the signal-to-noise-ratio typically becomes critical.

In the second embodiment of the method, at least one of the positions ofthe zero point which are assigned to all spatial dimensions in which theposition of the molecule in the sample is determined may be shifted assoon as in average p photons of the luminescence light have beenregistered at the present positions. p may be comparatively small oreven very small. Particularly, p may have a value which is not higherthan 30, not higher than 20, not higher than 10 or even not higher than5. It is to be understood that it depends on the value of p how far theat least one of the positions is suitably shifted, because p, due to thebasics of statistics, determines the precision at which the rates or theintervals in time of the photons of the luminescence light can bedetermined for the present individual positions of the zero point.Alternatively or additionally, at least one of the positions of the zeropoint assigned to all spatial dimensions can be shifted as soon as n×qphotons of the luminescence light have been registered in total at allpresent positions. Here, n is the number of the spatial dimensions inwhich the position of the molecule in the sample is determined. q mayalso be comparatively small. Particularly, q may be equal to or smallerthan 50 or equal to or smaller than 25 or even equal to or smaller than5. It also applies here that it depends on the value of q how far the atleast one position of the zero point can be shifted in a suitable wayupon reaching n×q registered photons.

In a further variant of the second embodiment of the method, theposition of each zero point is shifted as soon as m-photons of theluminescence light have been registered at the present positions of thezero point. Here, m may also be small or even very small. Particularly,m may be 30 or smaller, 20 or smaller, 10 or smaller or even 5 orsmaller down to only 1.

Particularly with very small values of m, it is to be understood that inshifting the positions of the zero point only significant photons of theluminescence light from the molecule are to be considered, if possible,which means that such photons are neglected which have been registeredbut which are to be allotted or attributed to a noise. If the zero pointis no ideal zero point in which the intensity of the excitation lightgoes down to zero, a rate of photons of the luminescence light from themolecule which is associated with a remainder or residual value of theintensity of the excitation light in the zero point may be regarded assuch an insignificant noise and deducted before the rate or theintervals in time of the photons is/are determined which is/are used asthe basis for shifting the positions of the zero point.

As already mentioned before, the entire preliminary local area, witheach position of the zero point, should be in a region of the intensitydistribution of the excitation light in which the intensities of theexcitation light in the intensity increasing region remain below asaturation intensity of the excitation light, above which a furtherincrease of the intensity of the excitation light does not result in ahigh intensity of the luminescence light from the singularized molecule.In the second embodiment of the method, it is preferred that a maximumintensity, i.e. an absolute intensity level of the excitation light, isalways adjusted such that the preliminary local area, with regard toeach position of the zero point of the intensity distribution of theexcitation light, is in a region of not more than 90% of the saturationintensity of the excitation light.

When successively shifting the positions of the zero point, the maximumintensity of the excitation light may successively be increased. Withsuccessively shifting the positions of the zero point, their distancesto the actual position of the molecule in the sample is reduced. Byincreasing the maximum intensity of the excitation light, the reduceddistances are newly distributed over a higher bandwidth of differentintensity of the luminescence light from the singularized molecule.

For example, the absolute intensity of the excitation light may beincreased such that a rate of the photons registered for all presentpositions of the zero point remains equal. This is equivalent to thatthe average interval in time at which these photons are registeredremains the same. Keeping the rate or the average interval in time at aconstant level by increasing the absolute intensity of the excitationlight may at least be striven for temporarily, i.e. for a part time ofshifting the positions of the zero point.

Particularly, the maximum intensity of the excitation light may beincreased by at least 50% in total while shifting the positions of thezero point. The maximum intensity may also be increased by at least 100%or up to three times, four times or multiple times its starting value.

In the third embodiment of the method, the excitation light, like in thestarting method known from WO 2015/097000 A1, is directed onto thesample with an intensity distribution which has at least one intensityincreasing region with a known strictly monotonic course of theintensity of the excitation light over a distance to a model point ofthe intensity distribution in each of the spatial dimensions. This modelpoint of the intensity distribution is arranged at different positionsin the sample in each of the spatial dimensions. For each position ofthe model point of the intensity distribution in the sample, theluminescence light emitted by the molecule is registered; and theposition of the molecule in the sample is deduced from the intensitiesof the luminescence light registered.

In the third embodiment of the method, in addition to the known method,at first a preliminary local area of the sample is determined in whichthe molecule is located. Then, (i) a position of the model point of theintensity distribution is determined in each spatial dimension in such away that the at least one intensity increasing region extends over theentire preliminary local area in the respective spatial dimension, and(ii) a further local area in the sample is determined, in which themolecule is located and which is smaller than the preliminary localarea, from intensity values of the luminescence light, which include twointensity values per each spatial dimension, one of the two intensityvalues per each spatial dimension indicating the intensity of theluminescence light registered for the at least one position of the modelpoint of the intensity distribution. The steps (i) and (ii), includingarranging the model point of the intensity distribution of theexcitation light at the positions determined or defined in step (i) andregistering the luminescence light emitted from the molecule for each ofthese positions, are at least repeated once using the further local areaas a new preliminary local area.

In this way, the position of the singularized molecule in the sample isvery quickly, i.e. on basis of a very small number of photons emitted bythe singularized molecule and registered, confined to a small local areain all of the spatial dimensions. The size of this small local areacorresponds to the precision at which the position of the singularizedmolecule is determined. It may without problem become smaller than 10 nmand thus clearly smaller than the diffraction barrier at the wavelengthof the luminescence light.

In the third embodiment of the method, the sample, even in thepreliminary local area of the molecule, is not scanned spatially, i. e.completely. Instead, the positions of the model point of the intensitydistribution are intelligently defined with regard to the preliminarylocal area based on the intensities of the luminescence light registeredfor the previous positions of the model point of the intensitydistribution, i.e. making maximum use of all information on the actualposition of the singularized molecule available from the registeredintensities of the luminescence light. In the third embodiment of themethod, the defined positions of the model point may even completelyspare the preliminary local area as such.

That the excitation light, in the third embodiment of the method, isdirected onto the sample with an intensity distribution which, in eachof the spatial dimensions, has at least one intensity increasing regionwith a known strictly monotonic course of the intensity of theexcitation light over a distance to a model point of the intensitydistribution may mean that the intensity increasing region is formed bydestructive interference which is differently strong at differentdistances to the model point. Further, the intensity of the excitationlight in the at least one intensity increasing region may increasestarting from zero, i.e. for example starting from a completedestructive interference of the excitation light. Then, the intensityincreasing region particularly includes small or low intensities of theexcitation light which just marginally stress the singularized moleculeby exciting it for emission of luminescence light. The intensityincreasing region may adjoin a zero point of the intensity distributionof the excitation light, which, at the opposite side in the respectivespatial dimension, is adjoined by a further intensity increasing region.The two intensity increasing regions can be symmetric with regard to thezero point. The zero point may be used as the model point of theintensity distribution of the excitation light which then has theadvantage to be close to the smallest intensities of the excitationlight which just marginally stress the singularized molecule. Generally,the model point of the intensity distribution of the excitation lightmay be any model point whose respective position in the sample can bedefined and which, correspondingly, may be arranged at defined positionsin the sample. If the model point of the intensity distribution of theexcitation light is a zero point adjoined by the intensity increasingregions, the intensity of the excitation light strictly monotonically,i.e. continuously, increases over each of these intensity increasingregions with increasing distance to the model point. Depending on thetype of the model point of the intensity distribution, the intensity ofthe excitation light may instead strictly monotonically decrease overthe intensity increasing regions with increasing distance to the modelpoint.

Independently on whether two intensity increasing regions adjoining azero point or any other model point of the intensity distribution of theexcitation light are symmetric with regard to the model point, bothintensity increasing regions may be used in the third embodiment of themethod in that, for example, positions of the model point on oppositesides of the preliminary local area are defined in step (i).

The zero point may be an ideal zero point formed by interference, inwhich the intensity of the excitation light actually goes down to zero.A lower remaining or residual intensity of the excitation light in thezero point, however, is harmless, particularly as it is no goal of thethird embodiment of the method to position the zero point, if present atall in the intensity distribution of the excitation light, in the samplein such a way that its position coincides with the position of themolecule in the sample. For the same reason, the zero point delimited bythe intensity increasing regions may generally also be made up byGaussian intensity distributions arranged at a distance in therespective spatial dimension, particularly by the intensity minimumbetween such Gaussian intensity distributions. Further, the at least oneintensity increasing region may also be provided by a flank of only oneGaussian intensity distribution. In this case, however, the center ofintensity of the excitation light focused into the Gaussian intensitydistribution is the only model point of the intensity distributionavailable but is quite far away from the small intensities of theexcitation light in the intensity increasing region which are ofparticular interest.

Even with an intensity increasing region extending in one spatialdimension only, the position of the molecule in the sample can bedetermined at a high spatial resolution in two or all three spatialdimensions. Similarly, with an intensity increasing region extending intwo spatial dimensions only, the position of the singularized moleculein the sample may not only be determined at a high spatial resolution inthese two but also in all three spatial dimensions. For this purpose,the third embodiment of the method has to be executed more than oncewith aligning the intensity increasing region(s) with different spatialdimensions. These executions with different alignments of the intensityincreasing regions may take place one after the other orquasi-simultaneously, like for example by repeating the steps (i) and(ii) only after having them executed at least once for all differentalignments of the intensity increasing region(s).

In the third embodiment of the method, the preliminary local area inwhich the molecule is located may be determined in different ways.Examples of this determination are given below.

That, in step (i) of the third embodiment of the method, the at leastone position of the model point of the intensity distribution in eachspatial dimension is defined such that the at least one intensityincreasing region, in the respective spatial dimension, extends over thepreliminary local area, means that the molecule is for sure located inthat region of the intensity distribution of the excitation light whichis influenced by the intensity increasing region with regard to theintensity of the luminescence light from the molecule.

That in step (ii) intensity values of the luminescence light areevaluated which include two intensity values per each of the spatialdimensions, one of which being the intensity of the luminescence lightregistered for the at least one position of the model point of theintensity distribution, does not exclude that the respective secondintensity value for the respective spatial dimension is the same valuefor all spatial dimensions so that in step (ii) in total only n+1intensity values are evaluated, “n” being the number of the spatialdimensions in which the position of the singularized molecule isdetermined. Generally, however, one additional intensity value can beconsidered per each spatial dimension so that a total of 2n intensityvalues is evaluated.

In order to determine in step (ii) the further local area in the samplein which the molecule is located and which is smaller than thepreliminary local area, the dependency of the intensity of theluminescence light which is emitted by the singularized molecule on thedistance of the singularized molecule to the model point of theintensity distribution of the excitation light is to be considered. Thisdependency results from the known course of the intensity of theexcitation light in the intensity increasing region strictlymonotonically increasing or decreasing in the direction of thisdistance, and also from the photo-physical process on which theexcitation of the molecule for emission of luminescence light is based.Thus, with an intensity increasing region adjoining a zero point formedby destructive interference and a photoluminescence on basis of a singlephoton process there is an approximately quadratic dependency of theintensity of the luminescence light emitted by the molecule on itsdistance to the zero point. With a photoluminescence on basis of a twophoton process, this dependency is even stronger and follows a functionx⁴. Practically, in the third embodiment of the method, the strictlymonotonic course of the intensity of the excitation light in theintensity increasing region has only to be known insofar as it has aneffect on the intensity of the luminescence light from the molecule.I.e. the dependency of the intensity of the luminescence light on thedistance of the molecule to the model point of the intensitydistribution of the excitation light has to be known to be able toconsider it in determining the further spatial area. This dependency,however, can be determined easily, for example empirically by scanningthe surroundings of the molecule with the intensity increasing region insmall steps.

That in step (ii) the smaller further local area of the molecule in thesample is determined from intensity values of the luminescence lightwhich include two intensity values of the luminescence light per eachspatial dimension does not only include the option of consideringdifferent rates of photons of the luminescence light but also the optionof considering intervals in time at which the photons are registered. Itis to be understood that the average value of the intervals in time atwhich the photons are registered for a position of the model point ofthe intensity distribution of the excitation light is equal to areciprocal value of the rate of the photons of the luminescence lightregistered.

In the third embodiment of the method, the steps (i) and (ii) are atleast repeated once, i.e. the local area in which the molecule islocated in the sample is at least two times reduced in size with regardto the preliminary local area. This means that in the third embodimentof the method the local area of the molecule in the sample is reduced insize at least twice with regard to its first approximation. There may,however, be further reductions of the local area in size in a same wayor in another way. The local area reduced in size obtained after the atleast two reductions in size of the preliminary local area may also beused directly to indicate the position of the singularized molecule, forexample as a center of the local area with the radius of the local areaas a possible position error.

The second intensity value for the respective spatial dimension, whichis evaluated in step (ii) of the third embodiment of the method, may bean intensity of the luminescence light registered for a second positionof the model point of the intensity distribution in the sample. Thissecond position may be on the same side as the at least one position ofthe model point of the intensity distribution or on another side of thepreliminary local area opposite to the at least one position of themodel point of the intensity distribution in the respective spatialdimension. In any in these variants of the third embodiment of themethod, the effect of the different intensities of the excitation lightin the intensity increasing region is recorded at two differentpositions of the model point of the intensity distribution of theexcitation light, and it is known where these two different positionsare located with regard to the preliminary local area in the respectivespatial dimension.

Considering the known course of the intensity of the excitation light inthe intensity increasing region, in combination with the distance of thetwo different positions of the model point in the respective spatialdimension, it is possible to deduce the actual position of the moleculein the respective spatial dimension from the two intensities of theluminescence light registered for the two different positions of themodel point. Also in this variant of the third embodiment of the method,there is no need to consider two separate or extra positions of themodel point per each spatial dimension with regard to the intensities ofthe luminescence light registered for them. Instead, for determining theposition of the molecule in two spatial dimensions, the positions of themodel point may be arranged in the corners of a triangle extending in aplane spanned by these two spatial dimensions, i.e. in only threepositions in total. Correspondingly, for determining the position of themolecule in three spatial dimensions, the positions of the model pointmay be located in the corners of a tetrahedron. Principally, twoseparate or extra positions of the model point per spatial dimension inwhich the position of the molecule is determined are also possible. Withregard to the aspect of determining the position of the molecule in thesample based on as few photons of the luminescence light as possible,however, the resulting higher number of positions of the model point inthe sample, for which the luminescence light is registered, may not beideal.

In another variant of the third embodiment of the method, the secondintensity value for the respective spatial dimension in step (ii) is ameasure of the relative brightness of the singularized molecule. Thismeasure may particularly be a maximum intensity of the luminescencelight from the molecule when excited with the excitation light or anintensity value directly correlated therewith. The maximum intensity orthe intensity value correlated therewith may be actually measured forthe singularized molecule, or it may be estimated for all potentialsingularized molecules with a certain value.

In the third embodiment of the method, the luminescence light for thedifferent positions of the model point of the intensity distribution inthe sample may be registered quasi-simultaneously in that the modelpoint is repeatedly shifted between these positions in the sample. Forthis purpose, the same intensity distribution of the excitation lightmay be shifted by means of a scanner. It is, however, also possible tonewly form the intensity distribution for each of the differentpositions of its model point in the sample, for example by means of aspatial light modulator (SLM) arranged in the beam path of theexcitation light. Then, at least insofar, there is no need of a scanner.Further, it is possible to shift the model point of the intensitydistribution of the excitation light in the sample in that theexcitation light is provided by completely or partially different lightsources one after the other. In all these possible variants of the thirdembodiment of the method, the model point of the intensity distributionof the excitation light may be repeatedly shifted between its positionsin the sample. It is to be understood that the luminescence light fromthe molecule belonging to the individual positions of the model point isregistered separately. The quasi-simultaneous registration of theluminescence light for the different positions of the model point of theintensity distribution of the excitation light has the advantage thatsubjecting the sample to the excitation light and registering theluminescence light from the sample may be aborted immediately if thephotons of the luminescence light registered for the individualpositions of the model point of the intensity distribution of theexcitation light already allow for reducing the preliminary local areain the sample, in which the molecule is arranged, by a predetermined ordesired measure.

A corresponding abort criterion may also be applied when continuouslyregistering the luminescence light for each position of the model pointof the intensity distribution of the excitation light in the sample.There are, however, cases in which simultaneously monitoring theintensities of the luminescence light registered for all positions ofthe model point of the intensity distribution of the excitation lightalready after a smaller total number of photons from the moleculeindicates that the preliminary local area may be reduced in size by thedesired measure.

If, in the third embodiment of the method, the luminescence light, foreach of the positions of the model point of the intensity distributionof the excitation light, is only registered until the intensities of theregistered luminescence light are determined for these positions at asufficient precision such that the further local area can be determinedat a size reduced by a predetermined value as compared to thepreliminary local area, this predetermined value may be in a range of 5%to 75%. Here, this percentage relates to the extension of the spatialarea in the respective spatial dimension. It is to be understood thatthe intensities of the luminescence light registered for the differentpositions of the model point of the intensity distribution of theexcitation light have to be determined the more precisely the fartherthe further local area shall be reduced with regard to the preliminaryspatial area. A lower reduction in size requires a lower precision ofmeasuring the intensities of the luminescence light for the differentpositions of the model point but more repetitions of the steps (i) and(ii) of the third embodiment of the method to achieve a same precision.Here, an optimization may be carried out with regard to the number ofthe photons of the luminescence light which are needed for achieving acertain precision in determining the position of the molecule in thesample.

As already mentioned, the entire preliminary local area, at eachposition of the model point, should be in a region of the intensitydistribution of the excitation light in which the intensities in theintensity increasing region remain below the saturation intensity of theexcitation light above which a further increase of the intensity of theexcitation light does not result in a higher intensity of theluminescence light from the singularized molecule. In the thirdembodiment of the method, it is preferred that a maximum intensity, i.e.an absolute intensity level of the excitation light is always set suchthat the preliminary local area, with regard to each of the positions ofthe model point of the intensity distribution of the excitation lightdetermined or defined in step (i), is in a region of not more than 90%of the saturation intensity of the excitation light.

With the size of the local area decreasing, the maximum intensity of theexcitation light may be increased. In this way, the local area reducedin size may be again distributed over the full bandwidth of thedifferent intensities of the excitation light in the intensityincreasing region and thus over the full bandwidth of the differentintensities of the luminescence light from the singularized molecule.

Particularly, the maximum intensity of the excitation light may beincreased by at least 50% over all repetitions of the steps (i) and(ii). It may also be increased by at least 100% or even up to threetimes, four times or multiple times of its starting value.

The steps (i) and (ii) of the third embodiment of the method may berepeated until the further local area, in the final execution of step(ii), is not larger than a predetermined precision. This predeterminedprecision may be in a range of 20 nm or smaller. It may also be smallerthan 10 nm. Even a predetermined precision in the order of 1 nm and thusdown to 0.5 nm is possible. In principle, the third embodiment of themethod has no inherent limit for or barrier to the precision achievablein determining the position of the singularized molecule in the sample.Circumstances of the respective individual case, like for example adecreasing signal-to-noise-ratio, however, may limit the precision whichis achievable in practice. Thus, getting below a predeterminedsignal-to-noise-ratio or a lower limit for an achieved further reductionof the size of the local area in which the singularized molecule islocated may be defined as an abort criterion for the repetition of thesteps (i) and (ii) in the third embodiment of the method.

In all embodiments of the method, the preliminary local area in whichthe molecule is presumably located may be determined in different ways.Examples are given in the following.

In all embodiments of the method, at the beginning of determining theposition of the singularized molecule, a larger area of the sampleincluding the singularized molecule may be scanned with the zero pointin each spatial dimension. The position of the singularized molecule maybe estimated from the course of the intensity of the luminescence lightregistered during scanning; and the estimated position may be used as abasis in defining the positions of the zero point in the sample. Thisspatial scanning of at least an area of the sample may be carried outwith a comparatively low intensity of the excitation light and incomparatively big spatial and small temporal steps, because the positionof the molecule, i.e. a limited local area in which the molecule ispresumably located, will only be coarsely estimated therefrom. Insteadof with the zero point of the intensity distribution of the excitationlight, the larger area of the sample including the singularized moleculemay also be scanned with a Gaussian intensity distribution of theexcitation light, i.e. with a simple focused beam of the excitationlight in each of the spatial dimensions at the beginning of determiningthe position of the singularized molecule. This corresponds toconfocally microscopically imaging the singularized molecule in thesample.

In another variant of all embodiments of the method, the excitationlight with the Gaussian intensity distribution is only directed point bypoint or on a circular or spiral track onto the larger area of thesample including the molecule at the beginning of determining theposition of the singularized molecule. The position of the singularizedmolecule is then estimated from the course of the intensity of theluminescence light over the points or tracks, and the estimated positionis used as a basis in defining the positions of the zero point in thesample. In order to limit the number of photons of the luminescencelight emitted by the singularized molecule, the Gaussian intensitydistribution may be moved very quickly and/or may be kept low withregard to the maximum intensity of the excitation light. In moving theGaussian intensity distribution on circular or spiral tracks, theintensity increasing region in the periphery of the Gaussian intensitydistribution of the excitation light may be used to subject thesingularized molecule to a low intensity of the excitation light only,which is, however, sufficient to determine a limited local area in whichthe molecule is presumably located by localization of the molecule.

In a further variant of all embodiments of the method, an area of thesample including the singularized molecule is all over, i.e. completelysubjected to the excitation light and imaged on a detector registeringthe luminescence light with spatial resolution, like for example acamera, at the beginning of determining the position of the singularizedmolecule. Then, the position of the singularized molecule may beestimated from the spatial distribution of the luminescence lightregistered with the detector, and the estimated position may be used asa basis in defining the positions of the zero point in the sample. Asthere is no need to limit the local area in which the molecule ispresumably located to a particular small size, a few photons from thesingularized molecule are sufficient for this estimation.

In all steps which may be carried out at the beginning of determiningthe position of the singularized molecule to estimate the position ofthe molecule or to determine a limited local area in which the moleculeis presumably located, a maximum intensity of the luminescence lightfrom the molecule when excited by the excitation light or an intensityvalue correlated therewith, which is a measure of the relativebrightness of the singularized molecule, can also be determined.

In all embodiments of the method, the luminescence light may generallybe registered with a spatially resolving detector, like for example acamera, or with a smaller array of for example 2×2 or 3×3 point sensorsonly. From the spatial distribution of the photons of the luminescencelight from the singularized molecule registered over the differentpositions of the zero point, the position of the singularized moleculemay additionally be determined by localization. Here, a differentposition of the molecule in the sample determined by localization mayindicate a certain orientation of the molecule in the sample, because,in contrast to the position of the molecule in the sample determinedaccording to the present method, the position of the molecule in thesample determined by localization is dependent on the orientation of themolecule. In all embodiments of the method, it has no effect where anrespective photon emitted by the molecule is registered for a respectiveposition of the zero or model point of the intensity distribution of theexcitation light. Correspondingly, in all embodiments of the method, theluminescence light may be registered with a point detector.

In all embodiments of the method, the sample, prior to determining theposition of the singularized molecule, may be subjected to a switchingsignal which singularizes the molecule with regard to neighboringsimilar molecules in that it switches the neighboring similarmolecules—in contrast to the singularized molecule—into a dark state inwhich they are not excitable for emission of luminescence light with theexcitation light. This dark state may be another conformation state ofthe molecules which is not luminescent. It may, however, also be anelectronic dark state. Alternatively, the switching signal may onlyswitch the molecule to be singularized out of a dark state into aluminescent state. The switching signal may be switching light withanother wavelength and another intensity than the excitation light. Itmay also have the same wavelength as or just another intensity than theexcitation light. Generally, the switching signal may also be theexcitation light as such.

A repeated execution of the embodiments of the method may be used fordetermining the positions of a plurality of molecules which areexcitable with excitation light for emission of the fluorescence light,which mark a structure of interest in the sample and which aresingularized one after the other. In another embodiment, this repeatedexecution of the embodiments of the method serves for tracking of thesingularized molecule moving within the sample. Here, in each repetitionof the embodiments of the method, may, an error area surrounding thepreviously determined position of the molecule may be taken as thelimited local area in which the molecule is presumably located. Theextension of this error area has to be adapted to the maximum movingvelocity of the molecule in the sample.

An STED laser scanning fluorescence light microscope may be used forcarrying out the embodiments of the method. Particularly, the STED lightprovided by the STED laser scanning fluorescence light microscope andcomprising a zero point with adjoining intensity maxima may be used asthe excitation light.

Further information with regard to possible embodiments of theembodiments of the method may be taken from U.S. Pat. No. 9,719,928 B2which is incorporated herein by reference. Every detail which isdisclosed in U.S. Pat. No. 9,719,928 B2 and which is not incontradiction to the embodiments of the method may also be realized as adetail of the embodiments of the method.

Referring now in greater detail to the drawings, FIG. 1 schematicallyshows an STED laser scanning fluorescence light microscope 1 with whichthe embodiments of the method may be carried out. In carrying out theembodiments of the method, not all components of the STED laser scanningfluorescence light microscope 1 will necessarily be used. The STED laserscanning fluorescence light microscope 1, however, includes allcomponents which are necessary or needed for carrying out theembodiments of the method. In using the STED laser scanning fluorescencelight microscope 1 for carrying out the embodiments of the method, alight source 2, which in a normal use of the STED laser scanningfluorescence light microscope 1 provides STED light, provides excitationlight 3. By means of beam formers 4, the excitation light 3 is formedsuch that it comprises an intensity distribution with at least oneintensity increasing region in the focus of an objective 5. In oneembodiment of the method, the excitation light 8 comprises an intensitydistribution with a zero point in the focus of the objective andneighboring intensity maxima on both sides in all spatial dimensions inwhich a position of a singularized molecule in a sample 6 is to bedetermined. The flanks of these intensity maxima provide the intensityincreasing regions which are used in all embodiments of the method. Thebeam formers 4 may comprise passive components only or an active optic,like for example a spatial light modulator (SLM). In carrying out theembodiments of the method, a further light source 7 of the STED laserscanning fluorescence light microscope 1, which in normal use providesexcitation light, may provide switching light 8 to singularize themolecule in the sample 6, whose position in the sample 6 is determinedafterwards.

Singularizing the molecule may be based on that other similar moleculesare switched with the switching light 8 into a dark state in which theyare not excitable for emission of luminescence light by the excitationlight 3. The switching light 8 is coupled into the beam path of theexcitation light 3. For this purpose, a dichroitic beam splitter 9 isprovided here. The intensity increasing regions adjoining the zero pointof the intensity distribution of the excitation light 3 are shiftedwithin the sample 6 by means of a scanner 10. Via a dichroitic beamsplitter 11 which, from the point of view of the sample 6, is arrangedin front of the scanner 10 luminescence light 12 from the sample 6 iscoupled out of the beam path of the excitation light, and imaged onto acamera 14 by means of an optic 13. The camera 14 is an example of aspatially resolving detector for the luminescence light 12.Alternatively, the luminescence light 12 from the sample 6 is forwardedtowards a point detector 12 with an upstream pinhole aperture 17 bymeans of a dichroitic beam splitter 15. The luminescence light 12 comingfrom the sample 6 is emitted by the singularized molecule which isexcited for emission of luminescence light with the excitation light 3.The process on which this emission of luminescence light is based isphoto-luminescence, particularly fluorescence. The sample 6 is arrangedon a sample holder 18. By means of the sample holder 18, the sample may,for example, additionally be movable in z-direction, i.e. in directionof an optical axis of the objective 5, to additionally shift theintensity increasing regions adjoining the zero point of the intensitydistribution of the excitation light 3 in this direction within thesample 6, particularly if the zero point is also delimited by intensitymaxima of the excitation light in z-direction. The sample 6 is imagedonto the camera 14 in such a way that a localization of the singularizedmolecule is possible from the spatial distribution of the photons of theluminescence light 12 from the molecule over the camera 14. With allembodiments of the method, the position of the molecule in the sample 6is, however, at least additionally determined based on the intensitiesof the luminescence light 12 registered for different arrangements ofthe intensity increasing regions or positions of the zero point of theintensity distribution of the excitation light 3 within the sample 6.

FIG. 2 depicts the intensity distribution 19 of the excitation light 3along a section in x-direction perpendicular to the optical axis of theobjective 5 according to FIG. 1. The intensity distribution includes acentral zero point 20 in which the intensity I_(A) of the excitationlight 3 does down to zero or at least down to nearly zero. Intensitymaxima 21 are neighbors to this zero point 2 on both sides. Between thezero point 20 and the intensity maxima 21 intensity increasing regions22 are formed. In these intensity increasing regions 22, the intensityI_(A) of the excitation light 3 increases from zero up to and beyond asaturation intensity Is. At the saturation intensity Is the intensityI_(L) of the luminescence light 12 excited by means of the excitationlight 3 reaches a saturation value I_(SW) above which the intensityI_(L) does not increase further. The intensity distribution 19 of theexcitation light 3 is symmetric with regard to the zero point 20, i.e.the intensity increasing regions are symmetric with regard to eachother.

FIG. 3 illustrates a limited local area 23 in the sample 6 in which themolecule 24 is presumably located. This local area 23 is a circle in thex-y plane. In order to determine the position of the molecule 24 in x-and y-direction, the zero point 20 of the intensity distribution 19 ofthe excitation light 3 is arranged at four positions A to D in the x-yplane with regard to the limited local area. Here, the three positions Ato C which are also designated as peripheral positions are located on acircular arc 25 around the limited local area 23, and they are arrangedalong the circular arc 25 at equal distances. The fourth position D ofthe zero point 20 is located in the center of the limited local area 23,and thus in the center of the circular arc 25. In other words, thepositions A to C are arranged in the x-y plane in the corners of anequilateral triangle, and the position D is in the center of thistriangle. The luminescence light 12 emitted by the molecule 24 due toits excitation with the excitation light 3 is separately registered forthe positions A to D of the zero point 20 in the sample. With arotationally symmetric shape of the intensity increasing regions 22around the zero point 20 in the x-y plane, the intensity of theluminescence light 12 registered for the different positions A to D ofthe zero point 20 only depends on the distance a of the molecule 24 tothe respective one of the positions A to D and on the course 26 of theintensity I_(L) of the luminescence light over this distance a, as it isdepicted in FIG. 4.

FIG. 4 also depicts the distances a_(A) to a_(D) of the molecule 24 tothe zero point 20 for the positions A to D and the intensities of theluminescence light I_(A) to I_(D) resulting therefrom. In that theseintensities are measured in the first embodiment of the method, theassociated distances a_(A) to a_(D) can be determined from the course26, and on this basis the position of the molecule 24 can be determinedwith regard to the known positions A to D. As the intensities a_(A) toa_(D) may each only be determined at a certain accuracy which depends onthe number of photons of the luminescence light 12 registered for thepositions A to D, the position of the molecule 24 may also not bedetermined exactly but only at a certain precision. As compared to thetotal numbers of photons of the luminescence light 12 needed for thispurpose, however, the precision at which the position of the molecule 24is determined according to the embodiments of the method is very high.It is particularly clearly higher than in case of localizing themolecule 24 on basis of a spatial distribution of the photons of theluminescence light from the molecule 24 which is detected with aspatially resolving detector like the camera 14 according to FIG. 1. Asan alternative to determining the position of the molecule 24 withregard to the positions A to D on basis of the distances a_(A) to a_(D),a function describing the course 26 may be fitted to the intensitiesI_(A) to I_(D) measured for the positions A to D, and the position ofthe zero point 27 of the fitted function may be taken as the position ofthe molecule 24 in the sample.

In actually testing the first embodiment of the method, the position ofthe molecule could be determined at a precision of about 1 nm based onless than 5% of the photons of the luminescence light which would havebeen necessary for localization of the molecule 24 at the sameprecision.

The variant of the first embodiment of the method depicted in FIG. 5 asa block diagram, after a start 28, begins with singularizing 29 themolecule. Next, the limited local area 23 in which the molecule ispresumably located is determined 30, for example in that the full sample6 is subjected to the excitation light 3 and in that the luminescencelight 12 emitted out of the sample is imaged onto the camera 14. Then, aprocedure 31 follows which consists of arranging the zero point 20 atdefined positions A to D and registering the luminescence 12 for thesepositions A to D. Next, the position of the molecule 24 in the sample 6is deduced 32 from the intensities of the luminescence light 12registered for the different positions A to D. A loop 33 in which theprocedure 31 and the step of deducing 32 are repeated may be used todetermine the position of the molecule 24 at an increased precisionprior to the end 34. In the loop 33, the positions A to D of the zeropoint 20 are shifted towards the position of the molecule 24 in thesample 6 determined in the first step of deducing 32, and the absoluteintensity of the excitation light is increased.

Often, however, the loop 33 may also be executed without arranging thepositions A to D of the zero point more densely to, for example, follow,i.e. to track, a singularized molecule 24 moving within the sample.Here, the positions A to D may every time be arranged around thatposition of the molecule 24 that has been determined in the previousstep of deducing 32. The local area 23 spanned by the positions A to Dhas to be set so large here that it still includes the molecule 24, evenif it has moved after the latest registration of the luminescence light12 as far as possible in the sample 6. A larger loop 35 includes therepetition of all steps 29 to 32 to always singularize another one of aplurality of molecules by which a structure of interest is marked in thesample 6. The sum of the determined positions of the singularizedmolecules 24 then describes the structure of interest in the sample athigh spatial resolution.

With regard to the second embodiment of the method, FIG. 6 illustrates apreliminary local area 23 in the sample 6 in which the molecule 24 islocated due to previous measurements. Here, this local area is a circlein the x-y plane. To determine the position of the molecule 24 in x- andy-direction, three preliminary positions of the zero point 20 of theintensity distribution 19 of the excitation light 3 are defined in thex-y plane with regard to the preliminary local area. Here, the positionsA to C are arranged on a circular arc which runs around the preliminarylocal area 23 at a distance so that in all spatial dimensions thepreliminary local area 23 is arranged between the positions A to C.Along the circular arc 25, the positions A to C are arranged at equalintervals. In other words, the positions A to C are arranged in thecorners of an equilateral triangle in the x-y plane. The luminescencelight 12 emitted by the molecule 24 due to its excitation with theexcitation light 3 is separately registered for the positions A to C ofthe zero point 20 in the sample. With a rotational symmetric formationof the intensity increasing regions 22 around the zero point 20 in thex-y plane, the intensity of the luminescence light 12 registered for therespective one of the different positions A to C of the zero point 20only depends on the distance a of the molecule 24 to the respectiveposition A to C and the course 26 of the intensity I_(L) of theluminescence light over this distance a, as it is depicted in FIG. 7.

In FIG. 7, the distances a_(A)-a_(C) of the molecule 24 to the zeropoint 20 and the resulting intensities of the luminescence light I_(A)to I_(C) are depicted for the positions A to C. If these intensitieswould be measured exactly, the associated distances a_(A) to a_(C) couldbe determined by means of the course 26, and on this basis the positionof the molecule 24 could be exactly determined with regard to the knownpositions A to C. However, the accuracy at which the intensities aremeasured depends on the number of the photons of the luminescence light12 registered for the positions A to C. A accurate measurement of theintensities I_(A) to I_(C) therefore requires that a high number ofphotons is registered for each of the positions A to C of the zero point20.

The second embodiment of the method goes another way. According to thisembodiment, relatively few and particularly only so many photons of theluminescence light are registered for the different positions A to C ofthe zero point that a conclusion can be drawn whether the respectiveposition A to C of the zero point 20 is still comparatively far awayfrom the molecule 24, i.e. whether the distance a_(A) to a_(C) is stilllarge, and whether the distances a_(A) to a_(C) of the differentpositions A to C of the zero point 20 to the molecule 24 are about equalor certainly different. Depending on the result of this determinationfor which just a few photons of the luminescence light from the molecule24 have to be registered at each of the positions A to C, the positionsA to C are shifted into the preliminary local area 23, as illustrated byarrows 228 _(A1) to 228 _(C1) in FIG. 6. For the positions A to C of thezero point 20 shifted in this way, the luminescence light 12 from themolecule 24 is registered again to carry out the determination oncemore. As the arrows 228 _(A1) to 228 _(C1) depicted in FIG. 6 shift thepositions A to C of the zero point 20 towards new positions A to C atequal distances to the molecule 24, equal rates or equal intervals intime of the photons of the luminescence light 12 will be measured atthese new positions A to C. Correspondingly, the positions A to C willafterwards be shifted further towards their common center, which isindicated in FIG. 6 by arrows 228 _(A2) to 228 _(C2). In practice, manyrepetitions of the steps of shifting the positions A to C andregistering the luminescence light from the molecule 24 for thedifferent positions A to C may be carried out for bringing the positionsA to C close to the molecule 24. Here, registering the luminescencelight 12 for the different positions A to C occurs quasi-simultaneouslyto determine as quickly as possible how the rates of the photons ortheir intervals in time are related to each other and to shift thepositions A to C in a suitable way as soon as possible, i.e. after aslittle as possible photons, with the purpose of bringing the positions Ato C closer to the molecule 24. It is to be understood that the numberof the photons of the luminescence light registered for each of thepositions A to C up to the next step of shifting is correlated with thesteps size by which the positions A to C can be suitably shiftedafterwards. Generally, not all of the positions A to C have to beshifted after each step of registering the fluorescence light. It isalso possible to only shift those positions A to C at which the rate ofthe photons is particularly high or at which the intervals in timebetween the photons are particularly small. This technique can bedeveloped further so that each position A to C is always shifted when acertain number of photons has been registered for it, whereas the otherpositions A to C for which this is not yet the case are not yet shifted.By means of the second embodiment of the method, the local area of themolecule 24 in the sample may be very quickly, this means particularlybased on a much lower number of photons than with a localization of themolecule 24 in the sample 6, strongly reduced in size. If the positionsA to C are already very close to each other, the local area enclosed bythem can be indicated as the position of the molecule+/−the precisionachieved. Starting from these final positions A to C of the zero point20, however, an even more precise determination of the position of themolecule 24 may take place, in that, for example, this position isdeduced from the intensities of the luminescence light 12 determined forthese positions A to C based on the course 26 according to FIG. 7.

The variant of the second embodiment of the method depicted in FIG. 8 asa block diagram, after a start 229, begins with singularizing 230 themolecule 24, for example by means of the switching light 8 according toFIG. 1. Next, the preliminary local area 23 is determined 31. In a stepof defining 232, the preliminary positions A to C of the zero point 20are defined with regard to the preliminary local area 23. Then, in aprocedure 233, the zero point 20 is arranged at the positions A to C,and the luminescence light 12 emitted by the molecule 24 is separatelyregistered for the positions A to C. In this procedure 233, while theluminescence light 12 is separately registered for the differentpositions A to C, the zero point 20 is shifted between the positions Ato C in such a way that the luminescence light 12 isquasi-simultaneously registered for the different positions A to C. Inthe following step of shifting 234, the positions A to C of the zeropoint 20 are shifted into the preliminary local area 23 depending on therates or the intervals in time at which the photons of the luminescencelight 12 have been registered for the different positions A to C. Theprocedure 233 and the step of shifting 234 are repeated in a loop 235until the positions A to C of the zero point 20 have approached theposition of the molecule 24 in the sample up to a desired measure orprecision. Then, in a step of determining 236 the position of themolecule 24 in the sample is for example determined as the local areadelimited by the final positions A to C. The steps 232, 233, 234 and 236inclusive of the loop 235 may be repeated in a further loop 37 to followthe molecule 24 as it is moving in the sample 6. This is called trackingthe molecule 24. In tracking, the positions A to C may always bearranged around the position of the molecule 24 determined in theprevious step of determining 236. The preliminary spatial area 23 whichis afterwards spanned by the defined positions A to C is to be selectedso large that it still includes the molecule 24 even if it has movedafter the last procedure 233 over a maximum distance in the sample 6.

Alternatively, in a larger loop 238 the steps 230 and 31 mayadditionally be repeated to successively image a structure of interestin the sample 6 marked with a plurality of similar molecules 24. In thiscase, the end 239 is reached when the structure of interest is imaged asa desired level of completeness.

For the third embodiment of the method, FIG. 9 indicates, for oneposition of the zero point 20 at x_(N) the resulting intensity I_(L) ofthe luminescence light 12 depending on the position x of thesingularized molecule in the sample. Over the intensity increasingregions 22, the intensity I_(L) increases from zero up to a saturationvalue I_(SW). In the third embodiment of the method this is used asfollows: From the distribution of the luminescence light 12 emitted bythe singularized molecule over the camera 14, which is registered whilecompletely illuminating the sample 6 with the excitation light 3according to FIG. 1, for example, a preliminary local area 23 isdetermined in which the position of the molecule in the sample 6 islocated. By positioning the zero point 20 by means of the scanner 10according to FIG. 1 at a position x_(N1), the intensity increasingregion 22 which is on the left hand side here is arranged in the sample6 such that it covers the preliminary local area 23. Then, whilesubjecting the sample 6 to the excitation light 3, the luminescencelight 12 emitted by the molecule located at the actual position x₀ isregistered and its intensity I₁ is determined. The accuracy at which theintensity I₁ is determined depends on the number of the photons of theluminescence light 12 which are registered for this position x_(N1) ofthe zero point. If the intensity I₁ as well as the saturation valueI_(SW) would exactly be known, the position x₀ of the singularizedmolecule could be exactly deduced from the known course of the intensityI_(L) over the distance to the zero point 20. With a limited number ofphotons which are registered for determining the intensity I₁, however,an error remains. Similarly, an error remains in determining thesaturation value I_(SW) from, for example, the photons of theluminescence light 12 emitted by the molecule and registered with thecamera 14 at the beginning. To the contrary, the course of the intensityI_(L) of the luminescence light 12 can be determined rather exactly.Close to the zero point 20, the course of the intensity I_(L), as arule, quadratically depends on the distance to the zero point 20 with anexcitation of the molecule for emission of the fluorescence light 12 viaa single photon process. Despite of inaccuracies in determining I₁ andI_(SW) it is thus possible to determine a further local area 324 basedon the measurement of I₁, in which the position I₀ of the molecule islocated and which is clearly smaller than the local area 23. Thisfurther local area 324 is depicted in FIG. 9 for certain error-pronemeasurement values of I₁ and I_(SW).

FIG. 10 shows how the knowledge of the further local area 327 is usedfor newly positioning the zero point 20 at the position x_(N2) in thethird embodiment of the method to determine the actual position x₀ ofthe molecule in the sample 6 at an even higher precision, i.e. at ahigher spatial resolution. For this purpose, the position x_(N2) of thezero point 20 is once again arranged such that the left hand sideintensity increasing region 22 extends over the local area 324. Further,the absolute intensity of the excitation light 3 is increased such thatthe saturation value I_(SW) of the luminescence light 12 is reached at asmaller distance to the zero point 20. Then, the intensity I₂ of theluminescence light 12 from the molecule is determined for this positionx_(N2) of the zero point 20. From this intensity I₂ and the saturationvalue I_(SW), a further local area 325 can be determined in which themolecule is located in the sample 6 and which is now smaller than thelocal area 324. This further local area 325 may then be used forpositioning the zero point 20 at an even further position in the sample6 to determine the position x₀ of the molecule in the sample at an evenhigher precision. The local area 325, however, already indicates theposition x₀ of the molecule in the sample at a much higher precisionthan the preliminary local area 23. In the actual practice of the thirdembodiment of the method, the position x₀ of the molecule in the sample6 can be determined at an error of an order of not more than of 1 nm.

Instead of determining the further local area 324, 325 from theintensity I₁ or I₂, respectively, and the saturation value I_(SW) of theintensity I_(L) of the luminescence light 12, the zero point 20 may alsobe arranged at two different positions x_(N1a) and x_(N1b) in the sampleto measure the associated intensities of the luminescence light 12 andto then determine the further local area 324, 325 from these twointensities and the course of the intensity I_(L) over the distance tothe zero point 20, without using the saturation value I_(SW).

FIG. 11 illustrates a corresponding procedure using a Gaussian intensitydistribution of the excitation light 3 which, due to the fact that nosaturation value is reached, also results in a Gaussian intensitydistribution of the luminescence light 12. The intensity increasingregions 22 are here found at the flanks of the Gaussian intensitydistribution. In order to reduce the preliminary local area 23 of theposition x₀ of the molecule in the sample 6 in size, the center of theintensity 326 of the Gaussian intensity distribution of the excitationlight 3 is arranged at two different positions x_(G1a) and x_(G1b) sothat each time the intensity increasing region 220 on the left hand sideof FIG. 11 covers the preliminary local area 23. For each of thesepositions x_(G1a) and x_(G1b), the respective intensity I_(1a) or I_(1b)of the luminescence light 12 from the molecule is registered. From theintensities I_(1a) and I_(1b) in combination with the course of theintensity I_(L) of the luminescence light 12 over the distance to thecenter of intensity 326, a smaller further local area 324 is determinedin which the position x₀ of the molecule in the sample 6 is located. Ithas to be considered here, that FIG. 11 is not depicted at the samescale as FIGS. 3 and 4 and that, in order to advantageously use as lowintensities of the excitation light 3 in the intensity increasing region22 as possible to stress the singularized molecule as little aspossible, the positions x_(G1a), x_(G1b) of the model point of theintensity distribution I_(A) of the excitation light 3 have to bearranged much farther away from the position x₀ of the molecule in thesample of interest than the positions x_(N1) or x_(N2) of the zero point20. This is due to the fact that the Gaussian intensity distributionI_(A) of the excitation light 3 has a full width at half maximum of thediffraction barrier at the wavelength of the excitation light 3 and thatthe regions of small intensity I_(A) of the excitation light 3 are aboutthis full width at half maximum away from the center of intensity 326,whereas the small intensities of the excitation light 3 and theintensity increasing regions 22 in the intensity distribution of theexcitation light 3 comprising the zero point 20 are directly adjoiningthe zero point 20.

FIG. 12 depicts the preliminary local area 23 of the molecule in thesample 6 in an x-y plane perpendicular to the optical axis of theobjective 5 according to FIG. 1. Around this local area, four positionsof the zero point 20 which is used as the model point of the intensitydistribution of the excitation light 3 according to FIG. 2 are arrangedat equal distances. If the intensity of the luminescence light from themolecule 24 is registered for each of these positions of the zero point20, it is possible to determine the further local area 324 therefrom.One of the positions of the zero point 20 depicted in FIG. 12 is just anoption which is diagrammatically indicated with the position in theupper right of FIG. 12. Correspondingly, in a next step of the thirdembodiment of the method, the further local area 324 can be furtherreduced by positioning the zero point 20 at positions adjoining thefurther local area 325 which indicates the position of the molecule 24in the sample 6 with an even smaller error. Here as well, one of thepositions of the zero point 20 depicted in FIG. 12 is just an optionwhich is once again diametrically indicated in the upper right of thefigure.

FIG. 13 shows another arrangement of the zero point 20 with regard tothe preliminary local area 23 and the further local area 324 each timeat three positions at equal distances. These three positions alsoinclude at least two different positions per spatial dimension x and yin which the position of the molecule 24 is determined.

The procedure illustrates in FIGS. 12 and 13 for two spatial dimensionsmay also be extended to three spatial dimensions. For this purpose, atleast four positions of the zero point 20 have to be defined for eachlocal area 23-325.

FIG. 14 is a block diagram of a variant of the third embodiment of themethod. After a start 328, the preliminary spatial area 23 is determined329. Then, positions of the model point, i.e. of the zero point 20 orthe center of intensity 326, are defined 330 for the determined localarea. In the following step 331, the intensity distribution of theexcitation light 3 is directed onto the sample 6 with arranging themodel point at the defined positions, and the luminescence light emittedby the singularized molecule in the sample 6 is separately registeredfor each of these defined positions. On basis of the intensities of theluminescence light registered in step 331, a further local area 324 isdetermined 332. Here, the saturation value I_(SW) of the luminescencelight from the molecule may additionally be used. Afterwards, it ischecked 330 whether the precision indicated by the extension of thelocal area 324 already fulfils a predetermined specification of thisprecision. If the step of checking 333 has the result that the precisionis not yet high enough, the steps 330-332 are repeated, wherein in thestep of defining 330, the new positions of the model point are definedwith regard to the further local area 324. If the step of checking 333has a positive result, the end 334 of the method of determining theposition of the molecule 24 in the sample 6 has been reached.

FIG. 15 is a block diagram of a method in which the method according toFIG. 14 is repeatedly executed with regard to its steps 329-333. Here, astep of singularizing 335 the molecules follows to the start 328. Then,in a routine 336 using the steps 329-333 the position of each of thesingularized molecules is determined. A step of checking 337 determineswhether a structure marked with the molecules is already imaged at asufficient level of detail. If not, some of the molecules which mark thestructure are newly singularized. If the marked structure in checking337 is regarded as sufficiently imaged, the end 334 is reached.

FIG. 16 is a block diagram of a repeated execution of the steps 329-333according to FIG. 14 for tracking a singularized molecule 24 in thesample 6. For this purpose, after the start 328, the present position ofthe molecule 24 is determined at the desired precision by executing thesteps 329-333. Afterwards, it is optionally waited 338, or the presentposition of the molecule in the sample is directly determined onceagain. With each of the repetitions of the determination of the positionof the molecule 24 by means of the steps 329-333, the latest previouslydetermined smallest local area of the molecule 24 in the sample 6 maycentrically be expanded to define a new preliminary local area which isthen used as the preliminary local area 23 for the next execution of thesteps 329-333. Here, the smallest local area which has been determinedat last has to be expanded such that the molecule 24 may not have movedout of the expanded local area in the meantime.

Many variations and modifications may be made to the preferredembodiments of the invention without departing substantially from thespirit and principles of the invention. All such modifications andvariations are intended to be included herein within the scope of thepresent invention, as defined by the following claims.

We claim:
 1. A method of spatial high resolution determining, in nspatial dimensions, a position of a singularized molecule in a sample,the singularized molecule being excitable with excitation light foremission of luminescence light, and n being 1, 2 or 3, the methodcomprising providing the excitation light with an intensity distributionwhich, in each of the n spatial dimensions, comprises at least oneintensity increasing region with a known strictly monotonic course of anintensity of the luminescence light from the singularized molecule overa distance of the singularized molecule to a model point of theintensity distribution, determining a preliminary local area in thesample which includes the singularized molecule, directing theexcitation light with the intensity distribution onto the sample, andarranging the model point of the intensity distribution, in each of then spatial directions, at different positions in the sample, separatelyregistering the luminescence light emitted by the singularized moleculefor each of the different positions of the model point of the intensitydistribution in the sample, and deducing the position of thesingularized molecule in the sample from the intensities of theseparately registered luminescence light, wherein (i) in each of the nspatial dimensions, at least one preliminary position of the model pointof the intensity distribution is defined such that the at least oneintensity increasing region associated with the respective one of the nspatial dimensions extends over the preliminary local area in therespective one of the n spatial dimensions, wherein (ii) from intensityvalues of the luminescence light which include two intensity values foreach of the n spatial dimensions, at least one of which being theintensity of the luminescence light registered for the at least oneposition of the model point of the intensity distribution in therespective one of the n spatial dimensions, a further local area in thesample is determined which includes the singularized molecule and whichis smaller than the preliminary local area, and wherein the steps (i)and (ii) are repeated at least once using the last further local area asthe next preliminary local area.
 2. The method of claim 1, wherein theintensity of the excitation light in the at least one intensityincreasing region increases starting from zero at the model point. 3.The method of claim 1, wherein the model point is a zero point of theintensity distribution which, in each of the n spatial dimensions, isdelimited on one side by the at least one intensity increasing regionand on the other side by a further intensity increasing region.
 4. Themethod of claim 3, wherein the at least one intensity increasing regionand the further intensity increasing region are symmetric with regard tothe zero point.
 5. The method of claim 1, wherein the second intensityvalue for the respective one of the n spatial dimension is the intensityof the luminescence light registered for a second position of the modelpoint of the intensity distribution which, in the respective one of then spatial dimensions, is arranged at another point on the same side ofthe preliminary local area as the at least one position of the modelpoint of the intensity distribution or at a point on an opposite side ofthe preliminary local area opposing the at least one position of themodel point of the intensity distribution.
 6. The method of claim 1,wherein the number of the different positions of the model point of theintensity distribution in the sample, which is defined in each executionof the step (i), is between n+1 and 2n.
 7. The method of claim 1,wherein the second intensity value for the respective one of the nspatial dimension is a saturation value of the intensity of theluminescence light from the singularized molecule when excited with theexcitation light.
 8. The method of claim 1, wherein the luminescencelight is quasi-simultaneously registered for the different positions ofthe model point of the intensity distribution in the sample in that themodel point is repeatedly shifted between the different positions. 9.The method of claim 1, wherein the luminescence light is registered forthe different positions of the model point of the intensity distributionin the sample only until the intensities of the registered luminescencelight for the different positions are measured at a sufficient accuracyso that the further local area can be determined by a predeterminedvalue smaller than the preliminary local area.
 10. The method of claim9, wherein the predetermined value by which the further local area inthe respective spatial dimension can be determined smaller than thepreliminary local area is in a range from 5% to 75%.
 11. The method ofclaim 1, wherein a maximum intensity of the excitation light is adjustedsuch that the preliminary local area with regard to each of thedifferent positions of the model point of the intensity distribution inthe sample is in a region of not more than 90% of a saturation intensityof the excitation light.
 12. The method of claim 11, wherein the maximumintensity of the excitation light is increased in at least one of therepetitions of the steps (i) and (ii).
 13. The method of claim 12,wherein the maximum intensity of the excitation light is increased by atleast 50% over all repetitions of the steps (i) and (ii).
 14. The methodof claim 1, wherein the steps (i) and (ii) are repeated until thefurther local area is no longer larger than a predetermined precision atwhich the position of the singularized molecule in the sample is to bedetermined.
 15. The method of claim 14, wherein the predeterminedprecision is in a range between 0.5 and 20 nm.
 16. The method of claim1, wherein, at a beginning of determining the position of thesingularized molecule, a larger area of the sample including thesingularized molecule is scanned with at least one intensity increasingregion or with a Gaussian intensity distribution of the excitation lightin each of the n spatial dimensions, wherein the preliminary local areais determined from a course of an intensity of the luminescence lightregistered during scanning.
 17. The method of claim 1, wherein, at abeginning of determining the position of the singularized molecule, theexcitation light is directed with a Gaussian intensity distributionpoint by point or on a circular or spiral track onto a larger area ofthe sample including the singularized molecule, wherein the preliminarylocal area is determined from a course of an intensity of theluminescence light registered over the points or the spiral track,respectively.
 18. The method of claim 1, wherein, at a beginning ofdetermining the position of the singularized molecule, a larger area ofthe sample including the singularized molecule is as a whole subjectedto the excitation light and imaged on a spatially resolving detector,wherein the preliminary local area is determined from a spatialdistribution of the luminescence light registered with the detector. 19.The method of claim 1, wherein the luminescence light is registered at aspatial resolution, and wherein the position of the singularizedmolecule is additionally determined from a spatial distribution of allluminescence light which has been emitted by the singularized moleculeand registered.
 20. The method of claim 1, wherein the sample, prior todetermining the position of the singularized molecule, is subjected to aswitching signal which singularizes the molecule with regard toneighboring similar molecules, in that the neighboring similarmolecules, after being subjected to the switching signal, are no longerexcitable with the excitation light for emission of fluorescence light.21. The method of claim 1, wherein the steps of claim 1 are repeatedlyexecuted for determining the positions of a plurality of singularizedmolecules which are excitable with excitation light for emission ofluminescence light and which together mark a structure of interest in asample.
 22. The method of claim 1, wherein the steps of claim 35 arerepeated for tracking the singularized molecule when moving in thesample.
 23. The method of claim 1, wherein STED light provided by alaser light source of an STED laser scanning fluorescence lightmicroscope is used as the excitation light, wherein a scanner of theSTED laser scanning fluorescence light microscope is used for arrangingthe model point of the intensity distribution at different positions inthe sample, and wherein a detector of the STED laser scanningfluorescence light microscope is used for separately registering theluminescence light emitted by the singularized molecule for each of thedifferent positions of the model point of the intensity distribution inthe sample.